The usual advice given about bullying these days, it seems, is to confront the bullying head-on. This runs into a problem, however.
Some bullies like to be confronted about their bullying. It serves as affirmation - “Yes, I’m getting through to the targets of my bullying. It’s registering, it’s having an impact on them. This is acknowledgement. I’m getting effective results.” It’s kind of like angrily confronting a stalker or writing an angry email reply to a stalker - it’s affirmation for the stalker.
So, ignoring bullying might not be good, but confronting them may just give them the affirmation they want. So, what would be a suitable response for this type of bully?
You’re asking a huge question which is impossible to meaningfully answer without knowing the age of the bully and the bullied and the circumstances of the bullying. How old is the bully? Is the bully subject to parental or institutional discipline? Can the bullied person defend themselves physically if it comes down to a confrontation? Etc.
Give a specific circumstance with details.
They won’t think its so great if you confront them with a baseball bat
For those types, simple confrontation constitutes positive consequences. Want it to stop? You need to apply negative consequences: detention, expulsion, job loss, fines, imprisonment, vigorous physical self-defense, or all of the above.
Feeding the trolls rarely ends well.
Any confrontation with a bully has to be effective confrontation.
The idea that some bullies see confrontation as reinforcement and some don’t is misunderstanding the issue. All bullies want to see your reaction and as long as your reaction is ineffective, that reinforces what they’re doing. For example “Just leave me alone!” is pretty much guaranteed to be an ineffective confrontation. No bully really wants negative consequences, though. They’re bullies because they’re inherently cruel cowards.
Each bully will be different in terms of what level of confrontation is necessary, and the appropriate (or available) responses will depend on each individual situation, as Machine Elf suggested.