Earlier quoted context omitted.
It's not unclear at all without the apostrophe, because in German, compound words are written without spaces. If it was indeed a bar that specialized in a drink called "Rosis", it would be spelled "Rosisbar". The space makes it immediately apparent that it's a bar operated by someone called Rosi.
Compare: - Sport Bar - Lounge Bar - Cafe Bar (All from real german bar names.) - Rosis Bar Rosis could just as well be a word like Sport, Lounge or Cafe.
Rosis-Bar = a bar serving (or otherwise related to) “Rosis”
Rosis Bar = Rosi’s bar