Many hotels and guesthouses can arrange bicycle hire, and some even do so for free. Otherwise, rates vary, but expect to pay between Rs 150 and Rs 250 per day, less if you hire for several days. Most of the local tour operators have bikes for rent; just walk down Royal Rd and see what's on offer.
There are numerous car-hire companies in Grand Baie, and there's ABC in nearby Pereybère, so you should be able to bargain, especially if you're renting for several days. Prices generally start at around Rs 1000 per day for a small hatchback. Find out whether the management of your hotel or guesthouse has a special discount agreement with a local company. Motorbikes of 50cc and 100cc are widely available in Grand Baie; rental charges hover at around Rs 500 per day, less if you rent for several days.