It would still be a government entity, just a different entity, so the creation of a transporation authority ( I presume through an act of the state legislature) would require funding which now comes come from fares, federal subsidy and city dollars.
Bus service can be argued is an amenity of city life that cannot be offered over a broader area due to economies of scale.
Routes should be adjusted to reflect the needs of today's users, but an authority doesn't mean it's free, it means an elected body no longer has to set fares or justify keeping the service going.
Watertown's original bus service folded in the 60s but was revived when sate and federal programs allowed.
An authority will require an executive director, so that would be good for someone.