A Bridging visa A (subclass 010) is usually granted when you apply in Australia for a substantive visa while you still hold one. It comes into effect when your current substantive visa ceases, so you stay lawful while you wait for the decision. While your substantive visa is still in effect, its conditions continue to apply.
The BVA does not support return travel. Home Affairs says that if you leave Australia while your BVA is in effect, it ceases on departure and you cannot return on it. To travel and come back while your application is processed, you need a Bridging visa B granted before you leave.