I get a lot of rips but hardly any of the bleed a lot, so mostly it's just some new chalk and off you go (though I must admit I'm a bit whiny and only do stuff like dismounts after I've ripped most of the time).
We once had a show where we were meant to do bars, and I've had this rip which hadn't healed over the past 2 weeks (even though I even stayed away from bars for a couple of days each week). for that show we had practice thurs, fri, sat, then show on sat and sun, and the rip just got worse and worse kind of like a rip within the rip, peeling of one layer of skin after the other. Surprisingly enough, dealing with rips turned out to be really mental. I knew I kinda had to do bars anyway, so it was far easier than expected to just ignore it. Should have taken a picture of my hands though because they did look really disgusting. Chalk helps a ton with the pain.