The vehicle has just had the radiator replace and bled(by me). When it was being bled, a good bit of water splashed onto the engine(serpentine belt area). A few days later, I was driving it and it began to overheat again and shut off before I could find a safe place to pull over. The car still turns over and runs, but it is down on power and runs VERY rough at idle--it almost sounds like a diesel engine. Any ideas?

Check each cylinder's compression. It may indicate a blown head gasket, warped aluminum head, or damaged valves.

Oh, also, the coolant in the tank continues to bubble as though air is in there, but I know that there is no air in the system

I had a Taurus/Sable V-6 and I also spent much time at my job in the late 90's working on them. What you are describing is almost certainly a blown head gasket or damaged head. Sorry.