So for the first time recently I've started being involved with finding support bands for shows our band is headlining. I was wondering what everyone's experience with this is like? So far I'm finding it to be a miracle that there is ever more than 12 musicians in the same room at the same time.

A big issue we are having is we are contacting bands to see if they want the slot and they say they need to check with the members, then its maybe 5 or 6 days before we hear back if they are free or not.

Personally I feel bad if we haven't responded to a promoter on the same day we were asked or the day after except in outstanding circumstances so having bands take so long and respond with 'We havent heard back from x' yet is frustrating (Yet seemingly common).
Been there - waiting on bands to get back to you can be a real bummer - I give bands 24 hours to get back to me, I let them know this up front, 48hrs for a big commitment, 400+ venue size and up, etc - after that I move on. You have to be UPFRONT with them, let them know you need to tell the promoter/club owner on X day, which means you need an answer by X or you have to move on.

I generally do not like seeking out a promoter w/o a complete or nearly complete bill. 2 out of 3 bands, etc. Get a semi-solid commitment from 2, or 3 other bands. Get a date and run wit it, that way when a band, and THEY WILL, drops out, its a quick fix and you're back on your feet.
1981 Gibson Les Paul Custom (Black Beauty)
1980 Marshall JMP 2204