
I'm similar except that I am left-handed so usually use the left front pocket.
It goes without saying that you want the body cap to be completely dust-free... lens rear elements usually have caps to keep the dust off them, but a body cap is usually a big flat piece of plastic that is perfect for collecting dust, hair, etc then depositing it back into your camera if you're not careful.
To the original question...
I get the rear cap off the new lens and hold it in one hand. With the other, I will press the release button on the mounted lens (sometimes need to use one finger of the hand holding the new lens), twist it off, and immediately pop on the new lens (which is ready and waiting right next to the mounted lens.) Take old lens, put free rear lens cap on it, and put in bag. Total exposure time is usually less than half a second, I'd say.
The tricky thing is when I go from M42 back to K-mount lenses, as that involves unscrewing the lens then using my fingernail to release the latch that holds the M42 adapter in place... then quickly mounting the lens again. In these cases, I make extra sure that I am blocking any wind as much as possible, but exposure times are more like 5-7 agonizing seconds!
I was at a wedding over the weekend, and there were 2-3 wedding photographers using D3s and big F2.8 zooms, and I was rather surprised that the lens changing technique involved standing the camera on the monopod straight up and facing out, removing the lens, putting it away, pulling out new lens, then mounting. Did I mentioned that this was about 20' from a beach on the Atlantic Ocean? And that there was a fair amount of breeze? Granted, the full-frame sensor won't show the dust quite
as badly but it will be there, and I just can't see how they could expect to avoid it with such a laissez-faire lens changing routine.