You’ll probably have to get a pair of Vise-Grip pliers and adjust them so that they clamp onto the bridge pin very tightly. Then twist and pull until you pull the pin out of the hole. I would then take the appropriate drill bit, carefully mark on the bit with masking tape how deeply you need to drill the hole, and drill out the hole before reinserting the pin. Drill the hole out deeper than you think you are going to need, so that you have some room to maneuver and so you won’t have to drill out the hole again at some time in the future.
If there is any rust on the bridge pin(there probably is), take some very fine sandpaper and clean it off. Be careful to use a drill bit that is slightly smaller than the diameter of the bridge pin. Use a micrometer on the bridge pin to get an exact reading in thousands of an inch, and then get the numbered drill bit that most closely corresponds to that diameter but is not larger than the bridge pin.