There's a bike path that starts at the ocean side of Oxnard Beach Park at Mandalay Beach Road at Beach Way and takes you south all the way to Hollywood Beach and Channel Islands Harbor. Alternatively you can just park at the Oxnard Beach Park and go from there. It is roughly 3/4 of a mile one way to Harbor Boulevard.
Cross Harbor Boulevard and make your way into Channel Islands Harbor, where you can ride all the way to the south end of the harbor.
Other options of course include parking at the Channel Islands Harbor somewhere and cycling your way up to the Oxnard Beach Park. And you can also pedal your way over to S. Victoria Avenue and take the bike lane all the way down to Silverstrand Beach (or even park at Silverstrand and ride your way up from there...though do take not that this is not a bike path). Have fun!