It's clear that "Dead Bart" is a fabrication of a poster on the website Creepy Pasta, but like most of these things, someone's going to act like it really did happen and they're just covering it up. Let's just look at the many reasons this tale is ridiculous.
For one thing, this is mentioned as being in the first season of the show. At that point, Bart may not have truly been the focus of the show (as was originally planned) but he was the one everyone was talking about, and the focus of the merchandising campaign, even into the middle of the decade with the book Bart Simpson's Guide to Life. There's no way they'd kill him off at that stage, and the episode is too depressing for him to simply return comedically in the next episode..
For another thing, who in their right mind would actually write an episode for a TV series that would involve an entire act with a family sitting around being depressed. Even Larry David wouldn't do that!
The tombstone thing is also ridiculous. I could buy that one celebrity's death could be accurately predicted, but every single celebrity who would go on to appear on the show, and later died's exact date of death and another date of death for everyone who hasn't appeared yet REGARDLESS OF WHETHER OR NOT THEY WERE CELEBRITIES AT THE TIME!?!?! Come on!
Oh! And then there's the story of him talking to Matt Groening at a "fan event" (really?) and following him after a panel or whatever. He'd have to be one charming guy for to do anything more than ask a couple of questions after he walks out the door, but a trade secret? From Matt Groening, someone who's got a reputation as being so stand-offish? No way!
On the other hand, why is a rumor about an episode of an animated series so creepy?
First, it's just called "Dead Bart." Two four-letter words in your face. It's not "the Death of Bart Simpson," or anything more artful than that, just "Dead Bart" like they're labeling something.
Second, while it's a tell that it's fake, the fact that this comes SO EARLY in the show's run, it kind-of becomes a relic (albiet a fake one) of a time when the Simpsons just FELT less magical and, in its own way, creepier. The animation was crap, there weren't as many surreal gags, guest stars were rare and sometimes it seemed like they were going for poignancy rather than anything else. It was almost like an experimental phase, but I think the Nostalgia Critic put it best when he called it "awkward." It doesn't escape my preview that they placed it right on top of "Moaning Lisa" which epitomizes this phase of the show.
Third, whoever came up with this rumor skirted the issue of The Simpsons being a comedy. They don't describe a single gag (unless the fact that they suddenly look all skeletal after a whole year of sitting at the table depressed) and it's not even really poignant. Again, this makes it less believable, but still creepier. It's just cruel, from Bart being described as having a "genuine anger and hatred toward his family" (why and how are left to our imagination) to the ending with the celebrity tombs where it loses all credibility.
How we imagine Bart demonstrates "genuine anger and hatred" toward his family is a personal thing and tells you something about yourself.
Another creepy thing is that the author makes a point in saying "there's no sign of Maggie or the pets," but doesn't outright say they died or anything. Did the people working on the episode just not feel like writing them in? Maybe, your imagination could assume that because the Simpsons actually spent a year in morning, they all died of malnourishment. Again: if they'd given us a violent end for Maggie or the pets, that might have taken away from Bart's death and been over-the-top.
This is one disturbing rumor, but thank goodness it's fake. It's also not really funny, though I found some of the details interesting.