As you can see, the Bride spends over half a day lying in the truck before her legs start working again and she is able to drive it the hell out of the garage.
So ... was Buck the only person working at the hospital that night? In the span of 13 hours, did nobody discover two fresh bodies lying in the middle of a suddenly missing coma patient's room? There must have been a shift change at some point -- at the very least, Buck's absence would have been noted, and we have to believe that a patient in the Bride's condition would be monitored pretty closely. When he didn't show up for roll call or respond to pages, and when they saw no updates on the Bride for the past half-day, hospital staff presumably would have sent someone to both look for him and check on her. Honestly, somebody should've tripped over those dead guys within 10 minutes of the Bride making it to the garage.
"Hey, this isn't where we store these."
With a murdered employee and a missing patient, that hospital would've locked down like the Thunderdome while the Bride was still lying in Buck's truck and staring at her feet. Regardless of whether they thought she was responsible (and they probably wouldn't have -- they'd find it way more likely that some lunatic had killed Buck and hauled her comatose ass off like a sack of potatoes), the cops would be covering all exits and combing the building looking for her.
"OK," you think, "but maybe it wouldn't occur to them to look in the parking garage. Maybe they'd be too worried about whether there was a killer loose in the building to go see if Buck's car was missing." Well, sure, we could buy that for an hour or two. But once they'd established that the killer and coma patient didn't seem to be in the building, they'd need to figure out how to track their asses down. And someone (either the cops or a super sleuth doctor) would definitely notice that Buck's keys were gone, because Buck's keys look like this:
And the vehicle they operate looks like this:
The cops don't even search it anymore. The Purell costs were breaking their budget.