Last night, I happened to note the times:

Left my house at 20:30 on the dot for 21:40 flight. It takes ~18 minutes to IAD. I parked in garage 2. I didn't take my normal spot so wasted two minutes. Noted the clock in the terminal at 20:58 just past the BA counter. I then placed a call from the A terminal at 21:09. So ~20 minutes from getting my parking ticket in garage 2. This is close to a best case scenario, although I had some slowpokes in the security line but the countdown clock was at 1:00 min for the A terminal shuttle. Add an extra 5 minutes for C/D.

I assume 06:10 will be a similar scenario to the calm of late night but I might wrong...... It does get very busy around 8 am.

So best case getting to C/D is 25 mintues from entering garage 1 or 2 with BP pre-printed and no luggage to check.