Can you bicycle on the trails?

Not the trails to the caves. But I believe they do have biking trails in the state park.

Old Man's Cave, Ash Cave, Cedar Falls, Cantwell, Whispering Cave, Rock House, etc are for foot traffic only- Here is information on the Hocking Bike Trail-https://thehockinghills.org/Mountain_Bike_Trail.htm

Yes there are bike trails in the area but as previously stated the trails to the caves and other attractions are one way foot traffic only.

https://thehockinghills.org/Mountain_Bike_Trail.htm#:~:text=Two%20mountain%20bike%20trails%20are,here%20for%20a%20printable%20map

There are biking trails but not at most of the park areas where people walk. Most people go to Hocking to bike the roads