At Woodward West Gymnastics Camp the trainers have had plenty of experience protecting hands for swinging bars. (They have over 100 gymnasts some weeks.)
Unless you have a system you like better, this is what you get when you go into the trainers room for “repairs”:
In practice, they seemed to work very well.
Of course athletic tape is very expensive. You would not want to make these on a daily basis.
Gymnastics Coaching.com 