According to " http://ordnet.dk/ddo " , BARE has several meanings, one of them is adverbial, and as a direct synonim, they put KUN ( a word that is exclusively an adverb.) Therefore I think they are totally exchangeable, in their adverbial roles.
mange tak! you are right, not always...I was checking both adverbs back to ordnet.dk, (and also in italki.com). My own conclusion is that you have to get used of differents examples in diff. situations to master it. Good news, I will never forget both adverbs!!! ;--)