Bale, who moved to Real for a reported world-record fee from Tottenham last year, has scored 14 goals in 29 appearances for the Liga leaders.
And, despite an injury-interrupted season, the 24-year-old Wales international feels he has significantly improved in his time at the club.
"Cristiano, at the moment, is the best player in the world for me," Bale said.
"We all know the level that he plays at, it's absolutely extraordinary. It helps me so much to play in an attack that Cristiano is part of.
"It's important for any footballer to be playing these high level matches. I hope that we are all going to improve in order to secure trophies this season.
"I have had a very good six months in Madrid. What has surprised me most in La Liga are the tactics.
"Everybody here can play the ball, pass and move ... there are no long balls like in England. I'm really enjoying this great league."
Real Madrid are still aiming for a treble, with Carlo Ancelotti's side virtually assured of progressing to the UEFA Champions League quarter-finals after beating Schalke 6-1 in the first leg of their last 16 tie.
They lead La Liga by three points and have qualified for the Copa del Rey final, where they meet rivals Barcelona.
"We can still win it all," he added.
"We're in a good position but we have to go game by game because there are a lot of matches left, including some very hard ones.
"There are some very good teams in the Champions League. All of the remaining sides are potential winners. The tournament's wide open, as everyone is so strong."
