I can't believe this: bullet stuck in barrel

I wouldn't worry about pushing it out backwards.

I have found that a long socket wrench extension works great for removing stuck bullets. Ust the 3/8 for .45 and the 1/4 for 38/9. Corners are all rounded and fills the barrel quite well so no worry about slipping. Slide it in and hit it good with a hammer and the bullet will come out.

DNS makes a good point about steel tools.

The socket extension is suitable so long as all edges are rounded and smooth (use a tool that hasn't been abused). SOcket extensions are usually quite readily available, will not break or stick like wood, wont deform like brass, and won't damage your rifling so long as you use the appropriate size in the barrel. Since they are steel, it will take only one or two taps instead of several more with brass and wood as the steel doesn't deform and/or absorb the energy. If the steel on steel concerns you, wrap it in a layer of electrical tape although this is quite unnecessary.