Tiger barbs often become much less nippy in larger groups. Usually it's recommended that you keep at least six. No guarantees, though; sometimes you just get a tough guy. You could either rehome the bully (or all three, since tiger barbs really prefer to be in larger schools), or add more barbs in the hope that a larger school will reduce the aggression.
You didn't mention if you have other fish in the tank. If you don't have any other fish, you could probably have a school of 12 in a 20-gallon. If you do have fish, try going to aqadvisor.com and typing in your stocking list and tank size, and see how many more your tank might support.
joy to the fishes in the deep blue sea
55, 30, 30, 20, 10, and 10-gal. freshwater tropical tanks