Bale struggled initially for form and fitness after missing much of pre-season following his world record move from Tottenham last summer, though he went on to develop a devastating understanding with fellow attackers Cristiano Ronaldo and Karim Benzema.
Yet despite scoring in both the finals of the Copa del Rey and the Champions League, the 25-year-old thinks there is a lot more he can give on the pitch.
"I want to improve every season: give more assists, score more goals, I want to improve everything," said Bale at a press conference in California.
"It was disappointing not being in the World Cup, but I had a seven-week break and I could do a full pre-season.
"My adaptation last year was hard because I had no pre-season. This season I feel I am training well. We hope the preparation will help us all to achieve the goals this season.
"When you first arrive it is difficult. But many of the players speak English and this has been very helpful to me. It was all a huge change. It took a little time, but over time I have found it very comfortable."
Bale also dismissed suggestions that the players are under more pressure after their cup double last season.
"It's an exciting time when you are the best team in Europe," said the Wales star.
"I do not know if there will be more pressure this season, but every member of this team wants to win everything. We are more hungry than ever. We also want to retain our Champions League title.
"The fact is that we have a great spirit in the team, we help outside and inside the club. It is difficult to repeat the challenge of winning the Champions League, but we hope to repeat it."