With prolific Portuguese Cristiano Ronaldo sidelined by injury, Bale stepped up to net his first treble since his £86 million move from Tottenham Hotspur and coach Carlo Ancelotti suggested the Wales winger's adaptation period was over.
"He is in good shape, he is confident and he is a very important player for us," Ancelotti told a news conference. "He performed very well today."
Bale's pre-season preparations were disrupted by the protracted negotiations over his transfer and he then picked up a minor muscle strain but now appears to be back to full fitness and eager to impress the Real faithful.
Saturday's haul was a so-called "perfect hat-trick" - a header and a goal scored with each foot - and was only the second La Liga treble by a Briton after Gary Lineker's for Barcelona in 1987.
Sports daily As acclaimed Bale on their front page on Sunday as "Prince of Wales" (Principe de Gales), while rival newspaper Marca went for the headline "Prince of Goals" (Principe de Goles).
"It is always a pleasure to score but even more when you are able to score a hat-trick at the Santiago Bernabeu," Bale told reporters after grabbing a match ball and soaking up a post-match ovation from the Real faithful.
"I am very happy here," added the 24-year-old. "I needed time to adapt after not having a proper pre-season but now I am improving.
"I want to continue improving and working hard in the matches and in training and learn from the best like Cristiano Ronaldo."
Bale still has some way to go to match Ronaldo's incredible goal-scoring feats and the former Manchester United forward remains the undisputed king of the dressing room and a hero to the notoriously demanding Real fans.
The 28-year-old has netted 14 goals in his last seven appearances for club and country and is favourite to scoop the FIFA Ballon d'Or award ahead of Lionel Messi and Franck Ribery when the winner is announced next month.
Ronaldo has proven himself in key matches against some of Real's biggest rivals in La Liga and Europe, something Bale has yet to achieve, and Valladolid turned in one of the weakest performances seen at the Bernabeu for some time.
Mired down in 17th in La Liga, their players gifted Bale his opening two goals with some woeful defending and failed to pick him up when he raced into the penalty area to clip home a Marcelo cross for his third late on.
Until Bale performs against Barca and Atletico Madrid in La Liga or the likes of Bayern Munich and Manchester United in Europe, some will remain unconvinced he can ever justify his record transfer fee.
"He has not yet adapted completely," Real great Alfredo Di Stefano told Marca this week.
"He is coming from England when they tend to play a longer game and he is better suited to that," added the 87-year-old.
"Here he is having to play with the ball at his feet, with short passes and he still needs to get used to it."