@kymme yes coz you need to be a PR or oz citizen to get medicare benefits. in terms of full work rights whilst on a bridging visa, you need to wait for the bridging visa grant letter from immigration to ensure that you have full work rights since you are currently on a student visa. If you will apply for BVA...
Bridging Visa A allows the holder to reside in Australia and gives the holder work and study permissions based upon the substantive visa they previously held. For example, if you held a Student Visa at the time you applied for a different substantive visa while in Australia, you will be granted a Bridging Visa A with the same work and study conditions as your Student Visa.
If for example you are on a temporary graduate visa then you applied for BVA, your work rights will be the same as your temporary graduate visa.