Do your exercises. Do your exercises. Do your exercises.
This is not to say you should to much more than you're assigned, just that you should do them religiously.
My surgeon spent 3.5 hours inside my left shoulder three years ago. It wasn't a labrum tear, so I can't speak too intelligently about your specific situation.
However, this should encourage you: I was playing bass two weeks after surgery. Mind you, I wasn't playing much, but external rotation was good enough that I was playing without pain.
That said, this was apparently an unusual recovery. The surgeon called me a rock star (no reference to the bass playing, really). I'd be concerned about a "big show" in a month. A little playing here and there will probably be possible, but extended work is likely inadvisable even if possible.
Cool Strap 1; EBMM Reflex 3; Fernandes 24; Squier Jaguar VM SS 91; Green 105; Crappy Bassist... 195; G-B 365