I've been riding bikes on the island for years and have luckily never even come close to an accident. I ride a 125 Vespa, a Honda CBR125 and a 900 Triumph. In summer, they are absolutely the best way to cruise past the traffic road blocks in towns and to enjoy the beauty of the open roads of the countryside. You have to ride sensibly and defensively and on NO account consume anything which will impair your judgement. One loss of concentration can end up in a very painful accident - given that most people ride without protective clothing in summer, that is absolutely rule number 1.
If you want to explore the island or park close to the town centres and beaches, a scooter is a perfect way to get around. I would strongly recommend renting one bike per person - many of the cheap 50cc bikes just aren't up to the job of carrying passengers safely. Especially in Formentera where the roads tend to be very sandy. Owners of a full car licence are entitled to rent a 125cc bike, which is a far better option imo.
Please take extra care at roundabouts because many people here on the island are under the mistaken belief that they can turn left around the roundabout from the right hand lane. It is a recipe for disaster, especially for motorcyclists if they suddenly swing across your path without indicating. If you're thinking of partying leave the bike at home and get a cab/bus. Otherwise, ride carefully, stay safe and enjoy the beautiful island of Ibiza.