It is used to talk about champagne in particular, but perhaps about all kinds of sparkling wine too - as far as I know, it's a wine-tasting term which does not refer to the wine itself (cépage, vignoble etc), but to its texture.
I'm not at all a professional in that industry but I reckon that "fine bulle" means the texture is light/sophisticated as opposed to rough/coarse.
To be honest you are throwing me a curve ball though - it's something I have heard so many times before, but I never really checked it out myself, so my definition of it remains vague - sorry!
No problem, that's great, I'll say fine sparkling wine until I hear otherwise. It fits the context, which is a room service panier gourmet provided by a hotel. I think they want to say that the wine is not necessarily champagne but it will be fizzy and of a certain quality. Thank you!