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Good shout on the wet vac, have a screwfix voucher so may go that route. Although I'm sure either way I'll be getting in a flap. Just to check, you're talking about not fully undoing the cap nut during the bleeding process to reduce the rate of water escaping? Obviously this has to be fully undone if removing the rad.
jambon-
Basically, when you start undoing the nut that connects the radiator to the system, nothing will come out because the bleed valve is creating a vacuum.
As you undo the bleed value, the water will start pouring out the side that you've undone.
so it's a balance between how much the bleed valve is open and how much the retaining nut is open as to how wet your carpet gets :)
TLDR: have access to the wrench at all times in case you run out of places to put the water.
Soul
No worries.
I would also recommend using a wet vac (if you have one). Much easier to keep the area dry if you use it to extract the water.
I have one of these and they work a treat.
Also - never undo the nut fully and keep the adjustable wrench handy to nip back up when you're changing bowl etc.