i think the dwarves left all their instruments at bag end, confident they would return one day and get them again

all dwarves get their instruments back but three

bilbo tries to convince them to take thorin's harp and fili and kili's fiddles bc he doesnt believe such things believe in his house (bc it hurts him every time he sees them) but they think its better if he holds on to them

on her way to erebor dis takes her son's instruments but agrees that thorin's harp should stay with him

he hides the harp away in one of bag end's many unused bedrooms and almost forgets abt entirely until he takes in frodo

the bedroom frodo ends up getting is where the harp is and before the little guy can even ask him what it is, bilbo moves it to his study and tries to ignore it when writing (he cried for the first few days)

one day he plucks a string out of curiosity but it snaps due to lack of use and he panics and immediately takes it to a luthier bc as if he's going to destroy the last thing he has of thorin

the luthier immediately assumes he's trying to learn how to play and they're not a harpist, but they tell him the basics and send him off with a book on music theory

when he gets back frodo immediately asks if bilbo can play the harp and he panics and scurries back to his study

when he thinks no one is looking however, he plays the harp in hopes that itll help him deal with his emotions

as expected, he sounds horrible but frodo wouldnt tell him that

one night when he couldnt get to sleep he goes to the harp and figures out the first few notes of misty mountains and almost woke frodo up with his shouts of joy

over the next few weeks he figures out how to play the whole song; not as good as the dwarves but enough to satisfy him

frodo eventually approaches his uncle as he's noticed how much happier he's gotten ever since the harp got fixed

now, i dont think bilbo could talk to anyone abt his quest and his deep sadness for thorin. hamfast maybe, but he wouldnt rlly understand yknow?

but bilbo tells frodo and he seems to understand and he looks at the harp with admiration: a dwarf king's instrument! at bag end!

he encourages his uncle to write their quest down as another way of maybe helping him cope: and to talk to frodo as well abt it

he knows what its like to lose someone you love too soon and bilbo helped him with it, why cant he do it back?

i had more to add but now ive forgotten it im too sad now lmao

also thorin's totally watching bilbo throughout all this and he's so fucking proud of his burglar for learning how to cope and for honouring his friends through music and text