
Puppies are horrible, little savages, piranhas on legs, as annoying as it is it's all perfectly normal. They learn to control their biting through the reactions of those they bite.
This article explains brilliantly how to deal with it when he's biting you, for your older dog you'll find he's already giving the pup feedback, by squealing he's teaching the pup that "ouch, that was too hard" He'll also be giving other subtle signs if you watch, turning his head away, maybe yawning, By keeping pup and older dog apart you might actually be prolonging the problem, older dog becomes so much more appealing if not there to play with all the time.
Did the pup actually break the skin of your older dog or did you just see blood on him? Most likely blood on the other dog after play is puppy losing a tooth.
What breeds are they both? I've had sighthounds and collies my whole life, and always multiple dogs at a time, a new pup is with the adults 24/7 with as little as possible interference from me, they learn as much from the other dogs as they do from me. I completely ignore most dog-dog interactions, when pup gets too OTT the older dogs will tell them off, it's important they (adults) know that they won't get in trouble for that. Baby puppies have 'puppy licence' almost carte blanche to do as they wish, depending on the adults this puppy licence expires at any stage between 3 and 7 months. Adult males can be particularly tolerant/soft, an older female will teach puppy manners much sooner.
Look at this little rat bag
pulling the old boys tail, the older dog here is very sweet and tolerant, but he gets pushed too far and tells puppy off