~ Aki - Fairy ~
As best as I can figure from collecting stuff, it seems like the inventory updates every two or three pages navigated through in Towns, potentially regardless of whether or not you tell Bludeau to send it over..
This is not the case with me.
When I pick up something in towns, like flowers or trash, it does not show up in my bag at all. The numbers for what I have collected that shows in my bag never changes and it never lets me send what's in there to my inventory. It's showed me the same amount of stuff in there for over a year now no matter how much I go around towns and collect things.