The world's most expensive footballer is into his third day's training with his new team-mates ahead of the weekend trip to Villarreal.
Bale has had just 31 minutes of competitive action this season - a substitute appearance in Wales' defeat to Serbia this week - and his national manager Chris Coleman has said the player is not ready to play 90 minutes.
But, speaking at a launch of Real's third kit, the 24-year-old insisted he will be ready to answer Carlo Ancelotti's call on Saturday.
"I feel good," he said. "I have been training in the last week with Wales. I have had two good sessions today and I got half an hour with Wales on Tuesday.
"Obviously I am a bit behind everyone else physically, but I am hopeful I can catch up as soon as possible.
"I think you will have to wait until the match to see whether I am picked or not. Hopefully I can get my fitness up straight away and hopefully get a place in the team."
Bale has been warned by Barcelona's Gerard Pique that it may take a while to find his feet in the Bernabeu dressing-room.
But the £86million man, whose fee eclipsed the £80m paid to Manchester United for Cristiano Ronaldo, says his welcome has been a warm one.
"It was amazing," he said. "He (Ronaldo) is a nice guy, and he made me feel welcome just like everyone else. I am just looking forward to getting on the pitch and doing well."
Pique earlier told Sky Sports' Fantasy Football Club: "You never know how he will adapt to a dressing-room like Madrid's with a lot of stars like Cristiano and (Karim) Benzema.
"I hope he can play well, but we will see. The first month will be more difficult, then it will be a bit more relaxed.
"Real Madrid is such an immense team - a big, big club. Everyone wants to know something about the players, about Bale too.
"When you're playing for a great team like Madrid, with a lot of pressure because you have to win every game, it's a difficult life."
Villarreal v Real Madrid is live on Sky Sports 2 this Saturday, kick-off 9pm (UK time).