There are no dedicated bicycle-only trails in Island Beach but there is a bicycle lane on each side of the park road. When the shore is less crowded it can be quite pleasant to ride to the park from some of the closer towns just north of the park entrance.During summer weekends a bike may be your only way in, as they will stop letting vehicles in once there are no more parking spaces.
You can get an idea of what it is like to travel from Point Pleasant to the entrance of Island Beach by going here.
There are a few bicycle shops in the area, as you could find if you do a local search using Yahoo. There are also places in Seaside Heights were you can rent bicyles by the hour or by the day, most are only open during the summer season.
If you are riding in the park stay on the right side of the road moving with the flow of traffic. This is in accordance with New Jersey law, which also stipulates: "anyone under 17 years of age that rides a bicycle or is a passenger on a bicycle...must wear a safety helmet." and "a bicyclist must obey all state and local automobile driving laws. A parent may be held responsible for the child's violation of any traffic law." and " Initial violators of the helmet law will receive warnings. For minors, the parent or legal guardian may be fined a maximum of $25 for the 1st offense and a maximum of $100 for subsequent offense(s), if lack of parental supervision contributed to the offense."