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This only works if you can make a convincing show of force to the bully, if you can convince them that there will be consequences to further attacks.
If you try to bluff a bully and fail (as is very likely, bullies generally have enough social awareness to pick their targets and to get away with bullying), the bully will punish you. Severely. Standing up to a bully with no credible defense or threat gets you pounded.
Instead, gather allies and confront the bully together. Cultivate authorities and destroy the bully's ability to get away with crimes or prohibited actions. Devise asymmetrical ways of retaliating, using any advantages you might possess. If possible, find ways to make your show of force without making an actual counterattack on the bully. That way you can maintain the moral advantage.
Don't escalate. Keep your responses proportional, even restrained, and your mind focused and calm. If you're more aggressive or harmful than the bully, you've either opened yourself up to being seen as the problem, or given the bully a justification to take even more harmful actions against you. Bullies often try to provoke this exact mistake, by getting their targets angry.
If the bully is a powerful group, which can't safely be confronted or resisted, it may be necessary to suffer some retribution, some punishment, and continue to confront or resist anyway, to send the message that no amount of retribution, however violent, will stop your resistance, or change your behavior.
Other similar things people say are:
"Oh, I was just curious."
"I was just asking a question!"
"Apparently you can't take criticism."
"If you can't take a little criticism, you shouldn't blah blah..."
"I'm just sayin'!"
"You need to touch grass."
"You take everything too seriously."
It's all the same redirection trick.
Complicating matters is the fact that not everyone who redirects this way is consciously aware of what they're doing and may not even have genuine malicious intent. People don't want to admit to any bad qualities... some people redirect like this so they don't have to admit to themselves that they were thoughtless or malicious.
That doesn't justify their behavior, however. It just makes it harder to correct.
You're not "too sensitive" for getting upset when someone purposely upsets you. It's not "just a joke". They know what they're doing. They're just hiding their bullying behind the label of joking so they can play innocent.