The rides I've seen (sometimes called "boogies") stick to the side roads and visit places to buy local trinkets and such. Those are anywhere from $40 to $75, depending on your Spanish, negotiating skills, and where you book them. On the resorts will be more expensive and the vendor will be less willing to budge on price. I've never been on one that was truly off-road (ie, requiring a helmet) so I don't know where to catch them.
Walking along Playa Bavaro you will find many stands and even more people walking and "selling" excursions, including boogies. I use quotes because some are legit but many of the guys walking and "selling" are really scams. The stands are safer bets, and booking at the resort is the most reliable method.