The Wales international has begun to win over any doubters in the Spanish capital after a slow start following his £85million switch from Tottenham Hotspur.
Bale was unable to make an immediate impact following his move to Santiago Bernabeu, but is confident his fitness concerns are now in the past.
"My adaption at Real Madrid is going well," he said at a promotional event for adidas.
"I feel comfortable with my team-mates and with the team. Everyone has made me feel very welcome.
"Now, after my small injury, I am completely recovered.
"It is important that we achieved qualificiation to the next stage of the Champions League and now we are mathematically there and looking at 100 per cent in the league."
Bale also reflected on Wales' chances of appearing at a major finals and feels that his country have a chance given the young players coming through into Chris Coleman's side.
"Wales have the potential to reach the World Cup finals in Russia in 2018," he said.
"I will be watching the event in Brazil at home, but we have a lot of young talent coming through so we will see what is possible soon."