The 24-year-old joined Madrid from Tottenham Hotspur on Sunday for 100 million euros (USD 131.97 million), a fee which made him the world's most expensive player, the day before the transfer window closed and after months of speculation about his future. (Agencies)
"It was a long time. It was very stressful to say the least," Bale said on Thursday.
"I knew their interest from the start and I was always confident the move would go through but obviously the chairman Daniel Levy had to do his business and do Tottenham well so I kind of understood that,” Bale said.
"But at the same time, thinking of myself, it was a hard time, it was stressful and I just had to be patient and try and focus," he added.
Bale is currently preparing for Wales's upcoming World Cup qualifiers against Macedonia and Serbia after being unveiled at Madrid's Bernabeu on Monday.
He has not played since July and missed most of Spurs' pre-season training due to injury, so is unlikely to play the full 90 minutes in either Friday or Tuesday's qualifier.
He rejoined his Wales team mates soon after being presented to thousands of fans as Madrid's latest "galactico" signing and said it was somewhat of a relief to be back among familiar faces.
"It's obviously been a whirlwind few days It's quite nice to come back, relax and get back to normality, really," the former Southampton player said.
Having set the Premier League alight last season with 21 goals in 33 league appearances, Spurs fans were hoping he would stick with the club and help them continue their push for a spot in the Champions League, having missed out to bitter London rivals Arsenal by one point.
However, Bale said once Madrid showed their interest in him he was determined to move and realise a boyhood dream, with a picture being revealed at his unveiling of him wearing a club shirt as a child.
"When I was younger I had some close friends and we always loved European football and Real Madrid at that time were the dominant force and we always watched Real Madrid," he said.
"I remember family holidays, we used to go Spain, and we'd bring back replica shirts of Real Madrid and wear them out and always pretend to be the players when we played in the park,” Bale said.
"It just started from there and I followed them since. Obviously the football they play, the team they are is amazing and it's just great to be there," he added.
The 24-year-old joined Madrid from Tottenham Hotspur on Sunday for 100 million euros (USD 131.97 million), a fee which made him the world's most expensive player, the day before the transfer window closed and after months of speculation about his future.