Rodriguez picked out Bale to set the tone from the second minute and increased the lead with a vicious free kick from a tight angle in the 39th.
After Karim Benzema made it 3-0 early in the second half, Rodriguez produced another brilliant strike with a bicycle kick to whip in his second goal in the 50th.
Bale was not to be outdone and struck a blistering long ball while on the run that hit the upright before landing in the net with two minutes left.
Barcelona leads Madrid by two points after two rounds, but it was Celta Vigo that took the overnight lead on goal difference after crushing 10-man Rayo Vallecano 3-0.
Madrid’s victory was a relief for new coach Rafa Benitez, whose league debut last weekend ended in a frustrating scoreless draw at promoted Sporting Gijon.
Betis, which also returned to the topflight this season, was no match for Madrid at its Santiago Bernabeu Stadium and with Rodriguez back in the starting lineup after Benitez had left him out of his first-choice 11 in Gijon.
“For me, I could care less about the debate regarding which player plays,” said Benitez. “I just want 11 players playing well. I want to enjoy the 5-0.”
Bale was the first beneficiary of Rodriguez’s return when he spotted the Wales winger unmarked and placed a lobbed pass for him to head in beyond former Madrid goalkeeper Antonio Adan.
The outclassed Betis barely weathered Madrid’s relentless push for a second goal until Rodriguez drove a strike in off the far post from a free kick placed on the line on the right side of the area.
Bale then crossed for Benzema, who was injured in round one, to head the ball home in two minutes after halftime.
It went back to Rodriguez to again ignite the crowd with his acrobatic shot, lifting up Toni Kroos’ pass before slamming in back into the net with his back to the goal.
Goalie Keylor Navas had his quiet night interrupted when Raphael Varane fouled Jorge Molina in the box, but he responded by smothering Ruben Castro’s spot kick in the 61st before Bale capped the lopsided win from long range.