Carlo Ancelotti’s men started the match with purpose, but after spurning a couple of early opportunities, creatively they looked short of ideas.
Ronaldo had initially been included in their squad after a second appeal against the red card he picked up at Athletic Bilbao, but his attempt to fight the ban was ultimately unsuccessful again.
Just after the half-hour mark, Asier Illarramendi scored his first La Liga goal for Madrid with a deflected strike, but they had to wait until the final 20 minutes for their second as Elche were at last undone by a stunning strike from Bale.
Substitute Isco completed the scoring with a finish from a tight angle in the final 10 minutes and Real’s 15th-consecutive home win all competitions keeps them firmly in the hunt at the top of the table.
Jese Rodriguez continued in Ronaldo's absence and Illarramendi replaced the suspended Luka Modric, while Elche named an all-Spanish starting line-up.
The hosts unsurprisingly tried to take the initiative early on and Karim Benzema was quick to force Manu Herrera into an important stop, tipping the Frenchman's low drive around his right-hand post.
Soon after in the 10th minute, Angel Di Maria went even closer directly from a corner as Herrera misjudged the flight of his delivery, but luckily for Elche the crossbar came to their rescue.
Real struggled to break their visitors down and although Jese fired just wide from the edge of the area, it was by no means a clear-cut opportunity.
After that fairly stagnant spell, Real eventually took the lead 34 minutes in. Benzema won a corner despite appearing to be offside and from the resulting set-piece Illarramendi's half-volley from 20 yards deflected off Manu del Moral on its way to goal.
Real found it even harder to break down their visitors in the second half. Ancelotti’s men dominated possession, but chances were few and far between at both ends of the pitch.
Bale summed up his under-par hour in the 61st minute as he charged down the right in an encouraging move, cut into the area and then blasted the ball high into the stands as their supporters groaned.
However he showed his true quality 11 minutes later. After being gifted space by the Elche midfield 30 yards from goal, the Wales star hammered a ferocious effort in off the crossbar.
Isco added a third for good measure in the 81st minute as he controlled Benzema’s pass in the area and squeezed a well-placed shot past Herrera from an acute angle.