It's a show on a budget?
In show reason? With all the damage the school should have from the vampire attacks, maybe they think the nearby bar is closer.
It's probably pretty fair to say there aren't a lot of venues to choose from in Sunnydale, unless you're down for abandoned warehouses or churches/graveyards. I could definitely believe the Bronze actually automatically functions as the central community/activity center of the town. And we see at various different times that the Bronze specifically has a desire for/system for underage customers, anyway, so it's never really presented as a purely adult venue.