You must be doing some pretty large boards to need a bucket. 20cm is about as large as I've ever needed, so I just use a plastic sandwich container. For the FC etchant, I would shine a light underneath, which would warm the etchant and also I'd be able to see when the etching was complete, because I could see through the board.
I don't see any benefit to the plastic bag and I can see it being a mess.
Ya, I have one bottle of FC and one bottle of AP crystals that I'll never use.
Here's a tip. Don't sniff the muriatic acid, like I did. That'll wake you up.