What does “bad rotors” mean? Are they rusted? Are they worn below specs? Are they warped causing uneven braking?
The new pads will wear quicker on used rotors since the rotors are “grooved”. As long as you stop reasonably quickly you should be ok. If you have extemely long stopping distances and poor braking performance then you are due for new rotors.
After about 200 miles your new pads and old rotors should be mated up as best as they ever will. If you have decent braking performance at that point you should be ok until you need another new set of pads.
Thin rotors can warp easily. They also don’t transfer heat as well and that degrades stopping heavy loads, on hills, and in emergency panic stops. As it is, you car is less safe than it could be. It is hard to tell if you are unsafe to the point of dangerous.