Sorry, didn't read the message last time.
Tokyo ESP comes to mind, which has the team from Ga-Rei (with their motorcycle) doing some scenes every now and then, but--
I'm not sure. Your description lacks a lot of details.
I assume the girl is the motorcycle rider?
It's possible you're referring to Fate/Zero as well, considering Saber has a motorcycle action scene (and looks like a highschool girl).
Its not golden boy I guess?
There was a very old anime about some armor (military tech); the protag got it thanks to a traffic accident while it was on transport and then the female lead and antagonist starts chasing him I think it also had a scene with arguing people suddenly getting interrupted by a motorcycle rider.