The chief concern is the same with any small puncture wound, infection. Some peroxide, betaine, etc... And its fine. As for how much it bleeds, depends on the size and species of snake, as well as how it actually bit you. Most bites are quick and defensive, and quite a bit of the time they don't even open their mouths, it is just a type of bunt. Occasionally I have had a small snake actually grab and wrap around my hand. Most non-venomous snakes actually have very small teeth, even the larger ones, so most actual wounds are so minor they stop bleeding in a few minutes. The only snake I have in the house that I would actually be worried about getting tagged by (when it's full grown) would be my emerald tree boa. Their scientific name, Corallus canninus, it's derived from the same latin word that gives us canine, and canine teeth.
I do get bitten once in. a while, but I really don't want to scare any possible new snake owners. I have a few baby carpet pythons that are just nippy, but growing out of it. Most common pet snake species aren't nippy at all if captive bred.