Ronaldo was forced to sit out a second consecutive game with a slight muscle strain, but his absence proved no problem for Madrid as Bale took his tally to eight goals in his last seven games.
Victory moved Real to within three points of La Liga leaders Barcelona and Atletico Madrid.
Bale opened the scoring with a simple header before also providing his sixth assist in his last seven outings for Karim Benzema to make it 2-0 before the break.
The former Tottenham Hotspur man added his second of the evening with a neat right-footed finish from Marcelo's cross before completing the perfect hat-trick by turning home another centre from the Brazilian full-back with his left foot.
However, the 24-year-old insisted he is no way ready to replace Ronaldo as Los Blancos' talisman.
"It was a massive blow not having Cristiano playing," he said.
"For me, he is the world's best player and we had to do a job (without him) and thankfully we did that.
"He has proven that not just with Real Madrid but with Portugal too and under pressure situations. He is a level above everyone else."
Despite the absence of the favourite to win this year's Ballon d'Or, Bale claimed to have not felt any extra burden on his shoulders to keep Real on the heels of Barca and Atletico.
However, he did admit to being desperate to seal his hat-trick after netting his second with still 24 minutes remaining.
"I didn't feel any pressure to be honest, I just want to go out there and enjoy my football and play as well as I can. I try to do that and thankfully I got a hat-trick.
"I think as soon as I scored the second I was trying to get the third, I was trying my hardest to get into positions and thankfully the move did work out and it was a great ball by Marcelo to put it on a plate for me."
Bale's form represents a remarkable turnaround in his brief time in the Spanish capital after a series of niggling injuries hampered his impact in the aftermath of his reported 91 million euro move ($124 million, £76 million) from Tottenham Hotspur.
And he believes the work he has done off the field to regain 100 percent fitness is beginning to pay off.
"I am happy that I am settling down. I am enjoying my football and I think that showed tonight. I feel part of the team.
"Every game that we play I am getting more used to it. I am enjoying it, which is the main thing.
"I feel my fitness is there now. Obviously I think I am going to keep improving, learning off the best, like Cristiano, and hopefully I can keep improving and doing a lot better as well."