Bridging may not be all that bad. The only time I bridged was following a TIA that I had in April -- the TIA was because my INR was lower than my meter reported it (and because I didn't increase my dosage when the INR appeared to be at bottom of range. My INR, taken at the hospital after my TIA was 1.7. I was discharged, taking a higher dose of warfarin, but told to bridge for a few days to compensate for my already low INR.
Sure, injecting Lovenox (or, in my case, the generic) into my abdomen was a bit of a pain -- but it wasn't all that bad. Fortunately, I only had to do it for a few days.
Depending on your procedure - and your doctor's requirements for bridging (or not), you may not have to bridge. In my experience -- and according to some protocols -- it's probably safe to be below 2.0 for a couple days. Of course, if you're having surgery, the surgeons probably are much more comfortable with minimal blood loss.