Bale enjoying Madrid life after slow start
Bale, who cost Real a reported 91 million euros ($123 million, £76 million) back in September, spent nearly a month on the sidelines due to a thigh problem.
However, he has made a blistering return to form in the past month with three goals and five assists in his last four games.
"It has been great ever since I have been here, everyone has made me feel very welcome," he said at a sponsor's event on Thursday.
"I felt very comfortable straight away, but obviously after an injury and a bit of a slow start I am now enjoying everything on the pitch now and I am just looking forward to the rest of the season."
The triumvirate of Bale, Karim Benzema and Cristiano Ronaldo have combined for 16 goals and 11 assists in Madrid's last four outings.
Whilst Carlo Ancelotti's men have hit top form, title rivals Barcelona have been struck by a series of injuries to key players, including World Player of the Year Lionel Messi, who won't play again this year.
And with Real's place in the last 16 of the Champions League all but secured, Bale is hoping they can eat into Barca's six-point gap over their title rivals in the coming weeks.
"I think it is important first and foremost that we qualify mathematically (in the Champions League) and we make sure get through that. But even with the Champions League, we're always 100 percent focused on the league as well. No matter what competition it is we'll be going out to win every single game."
Madrid suffered a serious injury of their own over the international break, however, with the news that Sami Khedira looks set to miss the rest of the season with a cruciate ligament injury.
Ancelotti has admitted that Khedira's absence could force him to switch from the 4-3-3 system he had struck upon since Bale's return.
And whilst he admitted the absence of his midfield partner is a big blow, Xabi Alonso is sure the German will bounce back.
"With the news about Khedira we were left in a state of shock," the Spanish international said.
"We were waiting for a few hours because we didn't know the exact extent of the injury that he had. Then the worst was confirmed, but he is very mentally strong. He is very German in that sense and I am sure he will be back quicker than they say.
"The 4-3-3 was a new idea which we had to adapt to, but it doesn't matter whether the system is a 4-2-3-1 or a 4-4-2. The important thing is that the players adapt to any system."
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