c = 1hr
2C = 30 min
3C = ( 1hr / 3 ) 20 minutes.
so a 3C battery is capable of discharging at a fast enough rate to drain completely in 20 minutes, according to specification.. some RC lipo cells are capable of 60C, ie : 1 minute discharge, or more.
Why does this matter ?. Well, if you plan to use the smallest possible battery that can power your bike, you need a battery capable of doing it without getting too hot.
a BMS needs to be sized big/powerfull enough to sustain the load of your motor controller *(ESC), so if you have a 20 amp controller, and plan to use 5ah ( 5000mah , same thing ), the battery needs to be capable of 4C, and the BMS needs to be capable of the same output , ie : 20 amps continuous.
If you use a high power battery on a low power motor, the battery will remain cool, last a long time, and life is good.
The motor will only get too hot if it's too small for the job, regardless of what battery you use.