But is it even legal to operate a bus route without a franchise? (Like operating a taxi without a medallion.)
My understanding (and I could be wrong here) is that you are conflating a franchise with a license.
The bus route in question is a franchise because it is being run within the MTA system (it’s labeled as “B-110”, it is marked on MTA bus maps, the MTA provides signage, etc.).
You can operate your own bus line (assuming that you have all the proper licenses, etc.) without being a franchise of the MTA, but your line won’t be listed on MTA maps/websites, they won’t provide signs at the bus stops, etc.)
The Wolf