I do pullups and lots of them. Trick is to always pair them with an opposing pushing motion -- I like handstand pushups, but any good overhead press ought to work. Typical is
MWF: 5 x 20
TR: 3 x 20
MWF vary grip within each set of 20. Yes regrab the bar. So some overhand, underhand, one hand reversed etc.
TR: Do much the same except try to do as many lopsided (so one arm does more work than the other) alternating. My goal is to work back to one-armed pullups. More than about 20 and all you are doing is getting more endurance. That's fine if you are climbing mountains then work up to sets of 50, but otherwise not much use.
Biggest tip I can give you: You are to think about the angle between your elbows and torso. Nothing else really matters. Oh I don't do too many wide grip because they make my shoulders hurt if I overdo it. YMMV
I've got tons of variations I do. Pullups are actually a pretty large topic. You can do them one-armed, with a towel, with a rope, plyometrically and even where you launch yourself, let go at the top and clap. At times for grins I do them with a belt and plates, but this is actually inferior to doing them one-armed.
Be advised that if you do them a lot you will get strong and you will also not really bulk up but look like a gymnast. If you want bulk you need to work on the separately. Pullups, however, are a staple and along with pushups/rows a necessity if you are going to stay strong.
If you have questions, feel free to ask. I'm just a gym rat so others might have better advice....