My suggestion is to add shortcut keys when hovering over a full bucket in the inventory to move the full bucket into the top slot of the backpack where you empty the bucket into the backpack's fluid tanks.

Example: Shift+A would move the full bucket from inventory into the top left slot and empty the bucket into the backpack tank. Shift+D would do the same for the right side when the other side is full.

This would make emptying buckets into the backpack much quicker and easier much like when there is a stack of empty buckets and Shift+LMB fills all of the buckets in the stack and puts them into the inventory.