OP, I don't understand what your first sentence means, "My wife’s boss is having his annual party and the regular band’s bassist can’t make it (a trio with no drums (I think)). So there's a band that regularly plays the annual party? Why do they regularly play the annual party? Who hires this band, or offers to let them play? Sounds to me like the party would be way better off with a free D.J. that will spin records (as it were) for drinks. The trouble with office parties is that suggesting such things can cause drama.
It sounds to me like about fifteen minutes into the party they're going to wish they had hired another band. One that takes more pride in what they play. Personally, I don't buy the idea of a "jam band". I don't understand what the allure or benefit of performing with people who "play on the fly" would be. Or, having to listen to them.
Note: I am not a fan of office parties. I actually hate office parties. Every time I went with my wife to a Pacific Bell office party, her boss who wasn't bad looking would get smashed and hit on me. Her bosses boss would get smashed and hit on my wife. A woman who befriended my wife at work and who definitely wasn't bad looking would hit on me, too. She and her husband invited us to stay overnight at their vineyard in Sonoma County, California, and there this woman also hit on me. That time, I got smashed.
How are you going keep your eye on your wife to protect her from all the #$%$# that goes on at such affairs if you on stage "jamming" with a band that "plays on the fly"? I think it's probably a vast conspiracy. Somebody is trying to get rid of you and distract you so they can hit on your wife.