A few things come to mind. Shared neutrals trip GFCI's. Sometimes this happens in a bathroom
GFCI's and AFCI's come in combination. A GFCI is a ground fault or it's tripped when the neutral and line currrent are unequal by about 7 mA.
An AFCI looks for a short characteristic or what can be perceived as arcing.
These are two different functions.
Your "Other rooms" may indeed be on the same circuit.
I would suspect that the treadmill doesn;t use a brushed motor.
1) See if the breaker is AFCI+GFCI. I'd almost want to determine the cause of the trip: 1) Overload, 2) AFCI and 3) GFCI, but I can't come up with an easy way to do so. A poor connection somewhere could easily be interpreted as an arc fault and a switch does ARC.
Does the other way trip it? Light on and then treadmill? Are we dealing with CFL lights?
Some AFCI breakers are known to be flaky. See; **broken link removed**
I have an Ideal Sure-test which MIGHT help, but only indirectly. Knowledge of the path and examining the path, so it's possible that a wall tracer and the Sure-test could help you find it.
One backstabbed outlet could be the cause of the issue.