When you say 'two characters' you mean two separate skeletons in the same project, or the same skeleton with two skins...?
If they're two skeletons they're treated as different entities, so their images and also their animations are not actually 'the same', even if they're identical in both.
So if that's the case you should be good by, not only keying an attachment hiding at frame 0 for that bag, but also stripping that image altogheter from the skeleton, if that character will never carry it.
If it's the same skeleton with two skins then that something you'll need to do at runtime side, I think. Wiser people around here would correct me if I'm mistaken.