I've only had the one procedure post ohs, and don't remember too clearly how the post op stuff went -I was on drugs y'know...That said:
Depends on what you are having done. If minor surgical, they may not want you to bridge after the procedure because of bleeding around the site (i.e., pacemaker replacement, big dental work (right, Ross?)) so you'd maybe be told to just start back on coumadin that evening after the procedure, and be back in range in 2-3 days. Really big surgical, you'd be in the hospital on heparin drip most likely.
If it's a colonoscopy with no surgery involved (archaic to require you to come off the coumadin, but that's another discussion) then you may be told to bridge a day or two afterward until you've had 2-3 days on coumadin and are back in range (although the lovenox will Frack up your INR monitor and show a Heparin error, so you can't get a reading).
I suggest you discuss this with your doctors.