You will definitely need something to snake down the bell throat to reach the mouthpiece. If you do not have something that will work, consult an instrument repairman (which might be the first place you should go as they can potentially get it out in a few seconds and may not charge anything at all). On the end of said snake, you could attach something that would go through the mouthpiece but get caught being pulled back (perhaps a bent paperclip? but it needs to be awfully small to fit through the mouthpiece, and getting it to go in the mouthpiece will likely be close to impossible). This is assuming that the mouthpiece is oriented as you said: the shank went in first.
My general advice is this: take it to a shop! It will save you time and will reduce the chances of damaging the instrument significantly if you have someone with the right tools do it.
Re: Emergency help needed with horn repair!!!! 06:32 on Thursday, March 03, 2011
Actually this happens a lot. Because that bell is so big and because lots of playrs take their mouthpiece out while they are puttingthe instrument away the mouthpiece will fall into the bell. If you have a french horn snake for cleaning the instruement you can do this yourself. But dont in from the bell like the mohthpuece did. Study the tubing and find a slide where you can insert the snake to go from inside to the outside of the bell and you can push the mouthpuece out from the inside. Another technique is to hold the french horn onits bell gently and apply ice or dry ice to where the mouthpiece is stuck when it gets cold apply a heat pad when it gets warm apply the ice again the temperature change will expand and constrict the different metals at different rates and the mouthpiece may just fall out.
If neither of these work then go to a repair shop and they should be able to get it out quickly and simply. i probably see this 2 or 3 times a year. Im surprised i dont see it more often actually.