This all depends very much on the set list. My mantra for these kinds of questions is that songs aren't made of tunings, they're made of notes. You only need a non-standard tuning if that's the only way to be able to hit the notes you need. If you're able to hit the notes, it doesn't matter how the guitars are tuned.
So for instance, it might be possible to play a full gig with a bass in drop-D or 1/2-step down; there may be some songs that could be played in standard tuning, but if you can still hit the notes on your downtuned bass, then you're good.
Me personally, I always bring two basses to a Mugshot Monday gig. For one thing, it's good to have a backup anyway. I can play the full gig on the five-string. The other bass is a 4-string (tuned standard) that I basically use on batches of songs that don't need the lower notes - just because I like it. Our guitarist brings four different guitars (one tuned standard, one a half-down, one in open G for Stones tunes, and I forget what the other's for), and we group songs in batches by which instrument he'll be using to minimize instrument changes. I try to keep it so I don't change instruments more than once per set.
One thing to bear in mind about changing instruments; if your cover band is trying to get people dancing, then dead air is the wintry blast of hell. I have timed it on gigs and you literally have four seconds from the time you end a song till the dance floor empties out, unless you get another groove going within those four seconds. FOUR. So keep instrument switching to a minimum and practice doing those switches as smoothly as possible.