The Welshman's first two months in Spain since his world record signing from Tottenham Hotspur on 1 September were overshadowed by fitness troubles, as he struggled to adapt to the squad after having an irregular pre-season.
Bale suffered two separate thigh strains in his first month at the club but has scored three goals and contributed five assists in his last four games for Los Blancos, who are third in La Liga and lead their UEFA Champions League group.
"I felt very comfortable straightaway," Bale told reporters at a promotional event in Madrid. "Obviously after an injury and a bit of a slow start I am enjoying everything on the pitch now and I am just looking forward to the rest of the season it's been great since I have been here, everyone has made me feel very welcome."
The 24-year-old scored his first Champions League goal for Madrid in a 2-2 draw with Juventus over a fortnight ago and next Wednesday will face Roberto Mancini's Galatasaray, a game from which Carlo Ancelotti's side require just a point to ensure they qualify for the second round of the competition as group winners.
Before that, Madrid travel to Almeria in search of three points to keep the heat on league leaders Barcelona.
The forward insisted he and his team-mates would not take their foot off the gas until they had qualified from their group and remained focused on catching Gerardo Martino's side, who are six points clear of Los Blancos, but who will be without goalkeeper Victor Valdes and top scorer and talisman Lionel Messi until January.
"I think it is important first and foremost that we qualify mathematically and we make sure we get through that, but even with the Champions League, we're 100 per cent focused on the league as well," Bale said. "No matter what competition it is, we'll be going out to win every single game."
Bale was speaking alongside Spain internationals Xabi Alonso and Alvaro Arbeloa and Brazil's Marcelo, all of whom will be involved in next year's FIFA World Cup™ in Brazil, unlike the Wales international.
Bale admitted his frustration at not being involved in football's biggest competition, but remained hopeful Wales could mount a challenge for the 2018 World Cup in Russia.
"Obviously it will not be nice watching everyone playing in the World Cup and being sat at home, but we have a good team full of young players that have come through together over the past few years, so hopefully in the years to come we'll be able to put together a strong challenge to qualify for a major tournament," Bale said.