Downplayed: Bob only has to show his best without any quitting attitude; it does not matter whether he defeat Alice or not.
Alice has realized the implications of orgasm in those with Super Strength, and is using 'able to beat me' as a rough way to determine if a potential love interest could survive sex with her. For greater awkwardness, her invulnerability also means that her 'nice tender lovemaking' is a normal person's 'rough sex.'
Lovers usually share a lot of common interest, and for Alice, bodybuilding and martial artist are two of her greatest passions,so she will only marry a man who is related to those things. Being that so, if a man wants to have anything with her, he must be up to the challenge and prove himself worthy, and besides, the part after the defeat open up the posibility for many kinds of kinky followup roleplays
It's a Secret Test of Character: If they really love each other, they'll hold back enough that neither is seriously injured.
...Until she falls In Love with the Mark, and can't bring herself to kill him. Fortunately the clan law has an escape clause stating she can reclaim her honor by bringing him back alive and as her husband.
Parodied: Alice can only have sex with men who defeat her... At strip poker!
Zig Zagged: Alice had a number of paramours over her lifetime, some who beat her in combat, some who didn't, and at least one who did defeat her but was so Gonk Alice refused him.
Discussed: "I don't think martial combat is a healthy basis for a relationship..."
Conversed: Two feminists talk about the misogynist implications of the trope.
Deconstructed: Alice is in love with Bob. Bob is in love with Alice. They can't get married because the law says she can only marry a man who defeats her: he's a wimpy Muggle and she has Full-Contact Magic.