Bequia is small enough that you do not need a car. Most visitors get around with a combination of walking, water taxis from the Port Elizabeth dock, and the local minibuses that loop around the island roads.
The minibuses (vans painted bright colours and pumping reggae) run informal routes for a flat fare of a few EC dollars; flag them down. Taxis are easy to find at the dock and are happy to do island tours for an agreed price.
Water taxis are the most enjoyable way to reach Princess Margaret and Lower Bay beaches from Port Elizabeth — a short open-boat ride across the bay for a few EC dollars. Drivers wait at the main dock; the trip back can be arranged on the spot. Renting a small Suzuki-style 4x4 for a day is worth it if you want to explore the north or the Moonhole side at your own pace.