The best way to dry the car out is to lift up the carpets as far as possible, leave the car in the sun (if you see any) with the windows slightly open and depending on where the most dampness is, place some rice (uncooked) on a thin tea-towel of kitchen towel over the area of fabric or carpet affected.
The rice will draw out the moisture... and if you use a tea-towel, it'll still be clean so you can use it for a chilli-con-carne afterwards and nobody will know..
The BCM is a cassette, so it will unbolt or unclip from its cage. You will also have to disconnect all the connector plugs but that's necessary anyway, to clean and dry them up. Take a photo of what plug goes where and how the wiring is arranged. The plugs will likely only fit to the BCM in one place, so you won't get confused where to plug it back in.. but it helps to see how the cabling is arranged.
The BCM may or may not be damaged internally.. It's basically a PCB inside a plastic box... so the tracks may have been corroded or damaged. If you can open the case, then that will help it dry out. Spray a bit of WD40 over it, and if you have a soft brush (an old make-up brush is perfect) then give it a "dust" to lift off the excess WD40 and any grit/dust .. but be gentle with it.
Then let it "air".. kitchen table overnight will do... and then refit it. Hopefully it'll be good and work.
I used to have a leaking windscreen on my old Alfa 155 that handily collected water and dripped it onto my fuse box... which reminds me; If you can't locate the leak for sure (does you car have a sunroof, fixed or opening?) then put a plastic carrier bag over the BCM to protect it from drips. Also make sure that no water can run downwards along the connector plugs... tie a piece of plastic around the cable so that any drips run down the plastic, rather than into the connector block. Lastly, don't wrap the BCM up too tight.. it gets warm so needs some ventilation to stop it overheating. If you definitely locate the leak, now or later... then you don't need to shield the BCM... that's what the plastic cassette is supposed to do.
Ralf S.