Will you be satisfied by a dictionary definition:

  buses, trains, subways, and other forms of transportation
  that charge set fares, run on fixed routes, and are
  available to the public.

I will agree, many taxi services are (in practice if not in principle) excluded by this definition. Discriminatory practices with how they select their fares, for instance. Also most don't have fixed routes so you'd have to relax that requirement to allow taxis (but some taxi shuttle services operate on more or less fixed routes).

I still don't see that as a materially useful definition but I'll admit I recognize the usage.

However, in the current context of discussing congestion—i.e. who gets to use the thing we all pay for—and other externalities like pollution and use of fossil fuels, public ownership is the salient thing to discuss.