My theory had been that Kaliba implanted a tracking device, then drove her to the hospital and put her in the driver's seat.
That was my theory, too. Sarah assumed it was Winston, but I figured they'd done it sooner rather than after they already had her in custody and were interrogating her with no intent of ever releasing her. Unless they anticipated the possibility of a heroic escape and lo-jacked her as a back-up plan, Scorpius-style. But if Sarah didn't have a transmitter in her already, then how did Winston know where and when to be to taser and grab her?

I still have a hard time believing a woman who was unconscious woke up and drove herself.
Yeah, I was under the impression that people who pass out from blood loss and are still bleeding don't tend to wake back up on their own.