There are campgrounds in the Columbia area but none in the immediate vicinity of RBSP.
There are no campgrounds at Rock Bridge Mem. SP other than a primitive group area reservable by groups such as scout troops. As tho other person noted, Finger Lakes SP has tent and RV camping, but that is about 10 miles north of Columbia.
We did not see the camping area while were in the park, but the park info states that there is some sort of special use area that might work if you have a group.
I think that Finger Lakes State Park, about 20 miles north, has camping facilities.
Get quick answers from Rock Bridge Memorial State Park staff and past visitors.