First, here in North Carolina it is legal to use a firearm in self-defense if you have a reasonable belief that you are in danger of being sexually assaulted, suffering great bodily harm, or being killed. Knives, clubs, bats, broken beer bottles, escrima sticks--any weapons I can think of--definitely fall into the criteria of inflicting great bodily harm or death. That's what weapons can do. You are justified in shooting. And while I suppose there could be additional circumstances where shooting, though justified, is not the best choice, I can't think of any that fit the given hypothetical scenario.
Bottom line: If the person is armed and actually threatening you, you are justified in shooting.
Second, if someone actually gets my gun--as in, I hand it to him--that would also give me a reasonable belief that I am in danger of suffering great bodily harm or being killed after he gets it.
Bottom line: The request itself could also justify shooting, if you have a reasonable belief that they could forcefully take your gun from you if you refuse.
Third, it's hard for me to picture a situation where the BG allows me enough room to draw my gun but does not allow me enough room to at least speed rock and fire.
Bottom line: If he gives me the time and space to draw, I will, and I will fire.
'Tis better to give than to receive, especially when it comes to bullets.