Was the good bolt that you removed locktited in?
If it is, (without the tools that would be necessary to remove the broken bolt), I'd say that you are better off selling your bolt carrier and buying a new one. Right now new bolt carriers are $40-$60. Get the $25 from the Poster that offered, buy a new one and don't look back.
If the broken bolt was not locktited in, Then the act of setting a reverse threaded drill bit on the top of the broken section stuck in the bolt carrier and spinning it with a drill should back the threaded stub right out of the bolt carrier, no additional tools necessary.
You should have a new carrier key, two new bolts, and a punch and hammer and a torque wrench to properly tighten ans stake the new bolts and stake the key to prevent them from loosening.