I know that in French, adjectives usually go after the nous, (major exception being BAGS adjectives), but I'm confused about the logic behind certaint adjectives having double meanings dependent upon their placement to the noun. For example, Chambre propre, "clean room", but propre Chambre is "own room". Is there a logical way to think about this to try and find a pattern, or do you just have to memorize it?
Short adjectives (one or two syllables) can be placed before or after the noun, notable exception to this being BAGS adjectives as you've noticed. A lot of them have different meanings depending on their position, but there's no general pattern to know the nature of this modification.
That being said, it seems that when the adjective is in front of the noun, it has often a moral or emotional meaning
Un curieux personnage -> An odd character
Whereas an adjective after the noun has frequently a descriptive meaning
Un personnage curieux -> A curious character
You can find a (non-exhaustive) list of adjectives which take different meanings here