Robben - who turned 31 on Friday - cancelled out Danny Latza's superb opener before Dante met the Dutchman's corner with a powerful downward header to put Bayern ahead on the stroke of half-time.
Second-half substitute Mario Gotze netted within three minutes of his introduction following a slick passing move involving Robben and Franck Ribery.
And Robben put the seal on fantastic individual display with a superb 20-yard curler 12 minutes from time before Sebastian Rode's close-range finish completed the rout.
Pep Guardiola will be pleased with the professionalism shown by his Bayern players, who return to Bundesliga action at Wolfsburg next Friday.
Latza put the hosts - 11th in the second tier of German football - ahead in style after just five minutes.
Stefano Celozzi's cross was only headed clear as far as Latza on the edge of the penalty area and he struck a sweet first-time volley across Manuel Neuer.
Bochum goalkeeper Michael Esser denied Robert Lewandowski and Robben saw a shot curl just wide before Bayern's positive response to going behind led to the equaliser.
Robben played a neat one-two with Thomas Muller that saw the Germany striker backheel the ball into the path of his team-mate to coolly slot home.
Bayern edged ahead when Dante slipped away from his marker to nod Robben's inswinging corner low past Esser.
Robben, Ribery and Gotze combined to allow the latter to make an instant impact following his 63rd-minute introduction from the bench.
Fifteen minutes later came the pick of the goals as Robben dispossessed a Bochum player, cut in from the right and curled into the top corner before he was substituted to avoid risk of injury.
Rode got in on the act with six minutes remaining when a failed headed clearance allowed him to poke home as Bayern were at their ruthless best.
