They'll laugh or taunt you in brackets and continue to do whatever it is you want them to stop as if you don't even exist.
I was lucky enough (or maybe avoiding CBers in general has its benefits) to have no confrontation with your character. I did however see some of her actions and I have to say, by all means, RP-wise she should be simply ignored. Your character is notorious for breaking laws of Yliakum, in the very middle of a large town.
Either what you do on the plaza is mere dueling; in which case people can ignore you all they want. If they don't want to accept, they don't need to.
Also: dueling in towns is a crime.
Or it's an open assault. In that case while a character wouldn't have choice other than to fight, if you happen to kill that character... here are some fun facts:
You're standing in the middle of a large town.
You just commited a crime, for which punishment (if notorious) may be even a permanent death.
Allow me to simplify:
Either the characters you challenge have all the RP right to ignore you, or your character should be non-existant by now.