There are ample opportunities for mountain biking in the park. From Trestles there is a trail that will lead you to the San Mateo Campground.
North of Cristianitos Road there are a number of miles of fire roads that wrap around the back of San Clemente and will eventually take to the end of Avenida Pico. You will encounter a fair amount of climbing on the fire roads so be prepare to work.
Running between, and below the fire roads is an extensive system of singletrack trails. Many of these trails are narrow and technical and are recommended for intermediate or advanced mountain bikers. Some of the trails are signed but the majority are not. It's a limited area so it's hard to get too lost. Heading uphill will eventually get you to the fire road and from there you can head South to San Mateo or North to San Clemente.
There are all kinds of trails for all levels and types of biking in California State Parks.
The Pacific Coast Bike Route passes directly through San Onofre State Beach. Casual riders can enjoy riding along the four-mile length of the park as well as the three miles between the end of the park and the Las Pulgas Gate at Camp Pendleton. If you are ambitious (and have a photo ID) you can ride through Camp Pendleton to Oceanside and points south. North of San Onofre State Beach the bike route passes near the famous Trestles surf spot before it continues into San Clemente.
It’s always a good idea to keep in mind these bicycling safety tips: Always wear a helmet. Keep to the right and always ride with traffic. Only ride on designated bike trails and obey all posted bicycle speeds as well as state laws. Ride a well-equipped bike. Look back before you pass or merge. Yield to pedestrians and other cyclists when appropriate. Be alert. Carry food, water, tools, patch kit, first aid kit and bike lock. Never travel alone in remote areas. And, of course, have fun and enjoy the sights that California State Parks have to offer.