If you're looking for some examples, in the Ontario area, Milton contracts out theirs. The City of Vaughan contracts out theirs. A number of municipalities do.
The fact is that most people don't know this, because when you contract out, the buses usually are painted with the city transit colours. They don't run as a Coach Canada bus or a Greyhound bus. They run as City of Vaughan buses, but they're actually owned and operated by a private company.