I have the tool but have never used it. I am betting it will not come out easily.
If you are not handy with tools I would not recommend trying because you will just bugger things up. Probably break the pins off too. I would use a drill press or even better, use a milling machine.
Johnny, I have replaced more BT-99 firing pins then you have fingers and toes. ALL bushings came out easy with a removal tool. Buy the tool on right which is for Brownings, the one on the left is a adjustable 2 pin for other European guns.
The bushing on my BT99 actually came loose and started to back out. It caused a few problems as you might guess. Unless it has rusted in place, I doubt anything more than the impact tool shown above by TOOLMAKER251 would be required and you might not even need that.
John, that impact tool I posted is a over kill for what is really required on the BT-99 which is a 3/8" drive. It's the only one I have for any bolt or nut that needs to be shocked. If you can find a 1/4" drive one, that would be more then enough.