Assuming that those public transportation systems use motorized vehicles, you really couldn't carry your holstered handgun on them without a CHL. (Probably hard to find an Amish horsedrawn taxi service or the like these days... )
You'd have to unload the ammo-feeding devices, case up the handgun, etc. as per Ohio law without the CHL.
Heck some of the city-run bus lines still have no-longer-legal signage prohibiting ALL firearms aboard, and likely won't give up that view until the case against the city of Cleveland (related but not on point) is settled in the Ohio Supreme Court, if then.