It is not okay to burp or pass gas anywhere in European public.

Where did you hear that?
It is okay and expected, to burp in Chinese (and possibly East Indian) culture as an indication that you've enjoyed your meal. Also, slurping of soup is fine too.
Thin Lizzy... you probably could've broken the ice already, since most women are loving and understanding of such things. Think it goes back to the animal world and scent marking of territory.

Hippos apparently spray their feces all over the place so guess we human females got lucky. My own personal motto has always been, okay for men to do it from day one, never for women.