The entrance fee is currently $10 per car, or $5 per bike, up to the per-car max of $10. However, for the paltry sum of $25, you can get an Everglades National Park annual pass that gets you (i.e. your car and everyone in it) into both Shark Valley and the Main Entrance South of Homestead for a full year.
Best Moon Over Miami Miami 2007 - Bike ride at Shark Valley
Actually, it's free any time outside of normal fee collection. Fee collection starts at 8:30 AM, so early morning rides are free, and they close the cash register about 4:30 PM. The park is open 24 hours a day, and it's fine to bike outside of fee hours.
You just park out on US 41 (frequently patrolled by the Miccosukee Tribal Police) and bike in. Be sure and park past the "No Parking" signs, because the Miccosukee police will ticket for illegal parking.
If you go during a full moon weekend, expect many fellow riders -- sometimes several hundred.