Rust bluing is not messy at all, you may get a bit dirty when you card the parts but that's why they make nitrile gloves. The first times I did it, I just hung the parts in the shop, boiled them in the kitchen and carded them on the front porch. Even my wife was impressed with how easy it was.
Later on, I built a cabinet where I can accelerate the rusting a bit. I use a spray bottle to wet the inside of it, then I heat it up. Once it's warm, I spray some water on the walls to raise the humidity, and it's good to go. When I'm in a hurry I just put a pot of water on the hot plate, and it will get hot and steamy in no time flat. The thermostat is a type you use in terrariums, simple, cheap and functional.
The pictures show it in a semi finished state, and the only major difference is that it now has a wire mesh tray above the heat bulb. I put a tin can on the shelf and pour a little bit of water in it, this will generate enough steam to maintain the humidity. It's not perfect, but it works and it only requires a minimum of baby sitting.