If I'm actually carrying the bag around, then the caps will be on both ends. If I am pretty much shooting from one place, so the bag is just lying on the ground, then I may drop uncapped lenses in there and carry on shooting. I generally minimise the need for rapid swapping by carrying two (or three) bodies with different lenses on. So, at an airshow for example, I might have the 10-22 on my crop and the 24-105L on my 5D in the morning for the flightline walk / static park, then switch to a combo with the 300 2.8L and 100-400L fitted for the afternoon air display.
I may decide that I want a shorter fast prime on at some time during the morning, for some shallow DOF shots, in which case I will switch one of the bodies over for a while. I will leave the caps off, if I plan to take the shots and then swap the lens back, put the caps on if I am going to leave it on for a while and wander around.
I don't baby my gear though, and if it comes down to getting the shots or putting the caps on, then I get the shots and worry about the gear later.