How to determine BJT switching time
Sure. Not all manufacturers specify the data for all their BJTs, but there are good data sheets around, for instance the 2SA2090.

Page 2 lists the delay times for a specific base current (Ton, Tstg, Tf):



(Source rhom.com)

Page 3 has a detailed test circuit and shows how to interpret the waveforms obtained using the test circuit:



(Source: rhom.com)