If you are a bully and about to make a debut, make amends before debut. That's the best.
Anyway, to answer your question and this is based on my friend's view who works in PR industry
- If the rumors are true, apologize publicly but make it vague. Never apologize directly for what you have been accused for (If you don't want to retire that is.)
- Try to contact the victim and reach a settlement. Get them to sign a NDA as part of the settlement.
- If no settlement can be reached, plant a fake victim. Get their claim to overshadow the actual claim and then disapprove it. People will naturally question other claims as well.
- If a settlement is reached, after a while, start circulating rumors about the celeb being wrongfully accused. Also, other speculations like a malicious ex-friend, ex-colleague or some kind of collateral damage. Nothing concrete but just enough to make people think she was not the bully.
- Lie low and make a comeback when time is right. Aka...some other celebrity or political scandal.
This sounds very immoral, I know.