Okay, this is only my 4th post here but when I saw the question, I HAD to post.
I purchased a vintage purse that arrived smelling as if it sat in an old musty mildewed basement for YEARS. There was no visible mold. I would have returned it but I loved the bag so much that I was determined to find a way to rid the bag of the smell.
For months, I tried EVERYTHING:
coffee beans
dryer sheets
filling the bag with newspaper
febreeze
scented satchets
lysol
baking soda
Nothing worked. I read somewhere that sitting the bag in direct sunlight would rid the bag of the smell. So, on the first warm sunny day of spring, I sat the bag on my porch (inside of a big brown box so no one could see what was in it). I propped it open so that the sun could shine inside of the bag and left it there for about 8 hours.
When I got home, I brought the bag inside of the house and smelled it. The smell was GONE!!! So...yeah, I said all of that to say....DIRECT SUNLIGHT.

Just make sure there isn't a chance of rain.