I believe your Student visa is not just cancelled. Your training provider would need to cancel your enrolment and notify immigration. I then think immigration contact you and ask something like give reason/s why your Student Visa should not be cancelled.
My guess is the time frame is in your favour and the Student Visa will expire - you would then have your Bridging Visa A in effect.
My guess is the time frame is in your favour and the Student Visa will expire - you would then have your Bridging Visa A in effect.