What version(s) of WoW are you using?

Retail

What problem are you experiencing that led to you asking for this feature?

There are certain items I'd like to keep in my bags rather than depositing them into the bank.

What solution would you like?

A Blacklist seems like the simplest solution to the problem. The item could be dragged and dropped into a UI element like when dragging items between groups/categories within the bag.

Any alternatives you can think of?

Have a list that the player has to manually add the item. Perhaps importable/editable outside the game with item IDs.

Anything else?

Without wanting to create feature creep on a single idea I do see the possibilties in adding various Depositing features - like being able auto deposit everything that's configured including gold, choosing which bank it goes into by default.

Your best bet is to use a search query to select the items you do want to deposit, say #reagent and then click the Transfer button to transfer just those.