"Buses" in general are not public property, publicly owned/operated buses are public property.
The reason that carry on a public bus is legal is because there is not a law against it, not because the bus is public property. Carry on a public bus in Ohio is subject to the same laws as carry in a private vehicle - a loaded handgun is only allowed if one possesses an Ohio CHL or its equivalent.
ok thanks..i believe ive got that cleared up.