I agree that a towel or a rubber mat might help.
But there is no need to wait to teach him to jump into the tub
When Chi was very young I taught her how to jump in and out of a small box ( google 101 things to do with a box - by Karen Pryor) It was a great game, she loved it, I had a blast teaching her and it easily translated into her jumping in and out of the tub on command when she was big enough
