TfL don’t train drivers. TfL don’t operate buses. Everything is contracted out.
Malcom – the thing you’re talking about is the “running number” – it identifies the shift the driver is working. Unfortunately not all companies use them on the side of the vehicle anymore (some stick them in the front windscreen).
Just get the time/date, route number & registration plate. When you complain to TfL, they’ll work out the company from the route number & then together they’ll be able to trace the driver.