Bale's qualities remind Rush of Los Blancos star Ronaldo and he has backed the player to prove himself with the nine-time European champions.
"I think he's quite similar to Ronaldo, but a younger version. He's got pace, he'll score goals from anywhere so hopefully he'll do well," Rush told The Mirror.
"People still want instant success but it might take him a few months to settle down but that's the way the world is now. Hopefully he'll get that time because he's a lovely lad.
"He had an excellent season last year, I think he'll do very well."
Bale failed to attend training on Tuesday.