I have an old WWI US Army-issue bugle with the mouthpiece rusted onto the body. what it the best way to get the mouthpiece off without hurting the rest of the instrument?
1.The best way is to take it to a repair shop! They might even fix it for free.
2.Otherwise there is a specific tool for separating mothpieces from trumpets that you could get (for instance the Bobcat Mouthpiece Puller which you find at for instance Amazon), but the first option is probably easier and cheaper if available to you.
Trying to fix it yourself in some other way using force, for instance by fixating the mouthpiece somehow and then trying to twist the horn, you'll run the risk of seriously damaging the instrument.
Watch this video to see how it's done (and how it shouldn't be done):