No need to replace the filter or the media. You can rinse everything in conditioned water and put it all back in there as far as I'm concerned. With no fish in there, you can start off with completely new water since future bacterial growth is done primarily in the filter, not the water.
When you say you cycled the tank with bacterial additive, does this mean you cycled with some fish in there or without anything in there? If you had no fish in there, a tank won't cycle at all unless there's a source of ammonia being added (such as pure ammonia, following instructions for a fishless cycle).
If you cycled with fish, it's important to check your water parameters pretty frequently to check the level of ammonia in order to keep it low. Cycling with fish means using the fish's ammonia to grow bacteria (unless you knew this already) and there are different instructions for doing that.
Thank you! I'll rinse it when I get home. I cycled fishless with pure ammonia, like I said I've been stalking around here and reading everything since I started my ten g. That one I had done a fish cycle and didn't want to do that again..