Neither does acting like you're saying. At least in my experience. In my experience, whenever I tried your tactic, the bully still stayed and responded with my sarcastic jokes with his, in a chain that only got interrupted when somebody else stepped in to restore order.
I believe your tactic doesn't work, and I also believe that passivity doesn't always work either (btw, regardless of what you say, it has gotten me out of bad situations in the past), and that's why I said the best solution would have probably been intimidation.
You've got to understand that what works for you doesn't automatically work for everyone, and bullies ain't a single kind, there are different types of them. There are those that give up when you "fight them with words", those who act like the complete opposite of what you described (like the ones I had to deal with), and so on. Everybody has to find the way to deal with them that works most for them. Me, I found that the "show indifference till they put their hands on you, THEN react" worked for my bullies. They wanted a reaction from me, and when they saw it would never come, they gave up looking for somebody else who would react instead.
The conviction that there is only one way to deal with bullies is what leads to bad advices and making some people's situations worse rather than better. Not that I'm accusing you of anything, I'm just telling you I use the method that I use because it's worked well in the past. Looks like this time I encountered an individual who required another type of treatment, and I wasn't prepared for it.
I hope you won't have the same experience of having to confront someone your method doesn't work with, because if there's something I've learned doing martial arts, is that there's always someone better than you. There's always someone who can outsmart your words, and/or that can kick your butt splendidly if it comes down to that.
