Incidentally, it's far from what you'd expect, but the US is actually probably more influential in public transport than private transport on an export basis; Cummins is very competitive in the diesel engine space for buses, and the ridiculously-named Wabtec (previously GE and Westinghouse's train-y divisions) is big in locomotive tech.

Though AIUI US companies are largely failing to keep up there, now, too; diesel city buses are on the way out, and electric bus powertrains are largely Chinese or European.