Am I to understand from this that when you say the topic came up, you just mean burping in general, not the fetish itself? Because if you have been with her that long and you’re having sex, it’s probably the right time to tell her everything, bro. And if you did tell her fully about your fetish, and that was her reaction, then I’d just say dump her, bro, because that’s ruthless.
There’s really no point in hiding it from her in the long run. And it’s hard to expect her to burp around you if she doesn’t even know you want her to or why you would want her to. It’s unfair to expect it of her if she doesn’t know about your fetish.
She may say she doesn’t burp around people in a relationship til she is deep into it, but by telling her your fetish, her point of view should change completely. I mean, if she CAN burp and she wants to be with you and be your sexual partner, then what possible reason could she have to deny you? It costs her nothing and brings enjoyment into the relationship. It’s literally a part of who you are and your sexual identity; if she cannot understand that, then why bother to continue things with her? You can’t just deny your burp fetish forever for her sake; it’s not healthy, man.
The only other reason she may not have to burp for you is that she can’t do it, fair enough, but you said you kinda noticed her doing some, and she also didn’t deny being able to do it when you brought up burping, so that’s a good sign.
Don’t be discouraged by her reaction when you talked about burping, it’s relatively meaningless in the grand scheme. If she wants to be with you and accept you as you are, her perception of burping will have to change, and the only way to do that is to tell her fully about the fetish. It may seem like a scary conversation, but it doesn’t really hold much risk, in my opinion; either way, you win.