A lot of the UK did this in the 1980s and it’s turned into such a disaster, most mayors and local authorities are trying to move to the London model: companies can bid a flat rate to deliver a bus service (effectively, they commit to providing drivers to deliver the timetable). TfL collects all fares. They also - I think - supply most of the buses to ensure they are of a certain standard, but the companies need to lease them, and maintain them.

This means you get private companies trying to lower costs and so costs are privatised, but the profits (if any) are socialised into a public authority.

This then allows TfL to offer system-wide passes making bus travel over all 43 boroughs cost effective.