Big-breasted girls with shy personalities and/or a history of being harassed for their "assets" by either lecherousmen or jealous women (i.e. D-Cup Distress) may tend to hide them from view, either by wearing baggy clothes or by outright suppressing with bandages, tight bras, etc.
Not to be confused with Suppressed Mammaries, where a woman (generally an actress) keeps her assets "at bay" temporarily and with a specific goal/task/purpose in mind.
Note: Not every convincing female crossdresser qualifies; possessing unambiguously large breasts is a requirement.
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Anime and Manga
Depicted as the article image is Heartcatch Pretty Cure character Itsuki Myoudouin in a one-off more or less "safe-for-work" omake page from an otherwise pornographic doujinshi. Do note, however, that while she is a Bifauxnen in Heartcatch Pretty Cure canon, she is actually not an example of this trope; the aforementioned doujinshi is simply exaggeratingly expanding on her Bifauxnen status for the hilarity factor.
Cosette Sara from Excel♥Saga is actually a child-sized adult with disproportionately sized breasts, which she somehow manages to keep hidden until late in the series. Too bad for the resident Lolicon, who until then had been lusting after her (he's totally Squicked out and leaves, to her disappointment).
Cosette: Actually, I'm... a G-Cup!!
Bleach has Isane Kotetsu and Captain Unohana; they usually wears a shihakusho, so we never really had an idea about what their chests looked like, until the Beach Episode came around.
In an earlier omake, Tatsuki revealed that she's actually a C-cup, it's just that standing next to the very well-stacked Orihime made her seem smaller than usual.
The Stern Ritter Bambietta Basterbine's uniform hides the fact she has an ample amount of cleavage, although her Dark Action Girl personality subverts the usual timidness associated with this trope. Also, her cleavage is revealed when she kills a handsome Mook after encouraging him to think they're going to have sex.
Although there is nothing canonical to indicate that she is actually embarrassed by it, Hinata Hyuuga from Naruto hid her assets under a baggy jacket Pre-Time Skip. This could actually be said to be symbolic for her hiding herself from others, especially her crush Naruto. Her clothing in Shippuden better displays her growth.
More accurately, after the Time Skip her breasts have grown so large that even her loose-fitting coats can't hide them very well.
Additionally Played for Laughs in the "Road to Ninja" manga special, in which she attempts to cover her bust, until Sakura assures her that there's no need to be self conscious. Cue Sakura getting very, very jealous.
Meguru from Hatsukoi Limited wears a too-small bra, and actively avoids both her favorite pastime and the guy she likes because she's embarrassed by her large breasts.
Tsukino Yukari from Ai Kora tries a similar approach, though she's quickly encouraged to not do anything that would interfere with her breathing and/or deform her breasts. Eventually, she gets more confident.
Gundam SEED's Lacus Clyne may not look like much at first glance, but by the time Destiny rolls around she's either grown rapidly in two year gap between the two series or she's a more well endowed than she lets on if the post-commercial intro is any indication. Subverted because the Lacus with the larger breast size was actually a Body Double named Meer Campbell. (And Meer's boobs are her natural ones, by the way.)
Double Subverted because the real Lacus actually is better-endowed than we were led to believe, just not to the extent as Meer.
The World God Only Knows has Yui Goidou, who tends to wear rather form concealing clothes like kimonos and later boy's uniforms. During her capture arc, a bored Keima briefly (and nonsexually) plays with them while bathing. In chapter 158, the goddess Mars attempts to weaponize this, to Vulcan's dismay.
In Genzo, crossdressing raised-as-a-boy Kiyone has this: to be specific, while disguised as Chiyomaru the disguise is flawless, but after The Reveal her breasts become much more noticeable.
Class president/magical girl cosplayer Mai Ootsuka in School Rumble is said by the boys in her class to be concealing a gigantic bosom, but she does a good job of keeping it hidden.
Hungary of Axis Powers Hetalia gets this most prominently on the cover of the most recent volume of the manga compared to having very obvious Boobs of Steel when shown later in-comic in a swimsuit. Truth in Television as she wears a military uniform on the cover, which is not an article of clothing meant to be very flattering.
Kazumi Yoshida from Shakugan no Shana, she does not look different from other students in her dresses, but ever since a bathroom scene where she is shown to have hidden her assets, her large breasts are used for Fanservice in every Beach Episode and parody that follows.
Hiida Sayuri from Best Student Council doesn't seem particularly large, especially when compared to some other fellow members of the eponymous student council. However, Puu-chan somehow gets a word of this and is the first to point it out, much to her chagrin. By the end of the episode in question, a swimsuit shot shows that she is indeed verywell-endowed.
In Saki Achiga-hen, Yuu Matsumi, due to being easily chilled as a result of her condition tends to wear thick clothing most of the time. It's not immediately obvious, but she has very large breasts, almost as large as Nodoka's.
H.E.R.O. (a revival of the old DC comic Dial H For Hero) sees the male (originally) protagonist transform into a tall, busty female superhero. After some turmoil, he (she?) loses the costume for a larger, more concealing Batman sweatshirt. In the later Dial H revival of the series, one of Manteau's stated reasons for wearing the same mask and long cloak whatever the Dial turns her into is to cover up overly buxom and Stripperiffic looks.
Cynthia of Malcolm in the Middle does this after hitting puberty and having a growth spurt in more ways than one, to avoid getting teased by her classmates. She wears a very heavy jumper. Malcolm, of course, finds out after Cynthia sets said jumper on fire by accident during an argument and has to get it off in a hurry. When Reese finds out, he tricks her into being his girlfriend, until Malcolm asks him if Reese knows what her name is in front of her, realising he's been caught he gores for broke and gives them a squeeze, which results in him getting the living crap kicked out of him.
Charlotte Marie Colde in Samurai Shodown actually has the same bust size as the infamously buxom Mai Shiranui; however she wears armor that hides that so you wouldn't know it. (Which makes Charlotte a surprising rare straight example of this trope in a Fighting Game.)
Vice from King of Fighters. Her measurements seem to indicate that her assets are slightly bigger than those of Mai Shiranui. But it's not at all evident (and she looks fairly flat too) when she's fighting in her usual tight-fitting office outfits.
Persona 4's Naoto Shirogane is hinted at being this in addition to being a Bokukko. When Rise is reading a doctors chart she is shocked at Naoto's bust size but is quickly shut up before she can say what it is. Her Hot Springs Episode picture does show there is more there than she normally lets on. In any case, while she most likely isn't completely flat, Fanon takes it Up to Eleven.
The anime also reveals that she is packing a lot under there (specially seen in the animated rendition of said Hot Springs Episode), but like the above, Fanon tends to exaggerate her bust size.
The sequel Persona 4: Arena has Akihiko complain that she's completely underdeveloped everywhere except her chest, but adds that that is just fat. In actuality, Akihiko doesn't say this. Labrys' Shadow makes Naoto think Akihiko is saying things that are designed to hurt her. While aware of this, she doesn't seem to like having it pointed out.
In Final Fantasy VII, Aeris is actually bigger than Tifa in this area, if you compare their models. Her modest dress and jacket, compared to Tifa's tight tank top, go a long way towards hiding this. This might, however be an artifact of the simplistic models.
Higher resolution depictions and official art more or less corroborate this. Tifa's a little bigger, but Aerith is by no means small.
Neptune is a slightly unusual case. Her usual body is teenaged and only modestly developed, but her Super Mode puts on about four cup sizes (and the be fair, about as many years in general). Given a nod when she loses her immortality at one point and freaks out over the idea of aging, saying outright she has her HDD form to use when she wants sex appeal.
Fate/stay night's Sakura Matou, of all people, turns out to be an E-cup note 85E to be exact, which when converted to American bra sizes is 38D, according to Taiga. It's not really visible outside of the H-scenes, though it's slightly more prominent in her casual clothes.
It's worth keeping in mind this is a Japanese E-cup, which has its letter derived from centimeters instead of inches and scales to the same ratio. Still well-endowed, but not as much as it sounds to an American reader.
Ayu from Kanon is a 17 years old teenager who looks like a elementary school girl, but when she takes off her cloak, you can see that her chest size is around as the other female leads. Her breast size is actually bigger than Shiori.