The Portugal international had trained alone in the build-up to the match due to the problem suffered in Wednesday's Champions League victory over Ludogorets, but he showed no ill effects to take his tally to 13 goals in six La Liga games so far this season.
It took just two minutes for Ronaldo to open the scoring with a close-range header and, after Karim Benzema had converted for the second, the FIFA Ballon d'Or winner was again on hand to finish off a crisp attacking move early in the second half.
Ronaldo was at the heart of Real's fourth goal, too, as he selflessly rolled the ball into the path of Benzema to give the Frenchman a second of the match on 69 minutes.
But, predictably, there was only ever likely to be one man who stole the headlines as Ronaldo scored his third - albeit controversially with the aid of his arm - in the 89th minute to add to treble against Deportivo La Coruna and a four-goal haul in a rout of Elche, all in just over a fortnight.
In netting his 22nd Liga hat-trick, Ronaldo also equalled the Spanish top-flight record held jointly by Telmo Zarra and Alfredo Di Stefano.
Real's fourth successive league win lifts them up to fourth in the table, while Bilbao's winless run was extended to seven games in all competitions as pressure begins to build on coach Ernesto Valverde.
The Basque club have not won a competitive game since the end of August and remain in the bottom three after this defeat.
Madrid's pace in attack continued to cause Bilbao plenty of problems and Ronaldo saw a low shot well saved by Gorka Iraizoz prior to Benzema failing to convert two good crosses from Bale.
Having spent the opening 20 minutes chasing shadows, the visitors slowly began to settle into the game, but only Iker Muniain's 23rd-minute strike tested Iker Casillas, the goalkeeper easily tipping over a dipping effort.
They did not have to wait long for the third goal, though, as Bale was released by Benzema before laying the ball on for Ronaldo to tap home his second.
The visitors were barely seeing anything of the ball and with 20 minutes to play they were further behind as Ronaldo raced clear before rolling a pass to Benzema, who applied the simplest of finishes.
Iraizoz's goal remained under threat despite Real's big lead and the goalkeeper made good saves from Ronaldo and Bale in the closing minutes.
Ronaldo's attempts to get his hat-trick saw Iraizoz punch clear a free-kick in the closing minutes but the attacker's moment finally arrived when he deflected a Pepe shot into the back of the net with a minute to go, although replays showed the ball may have come off his elbow.
