Time spent in the Pussy Wagon

When Beatrix wakes up it's night. You understand it because everything is dark. When we see the scene of Beatrix laying in the bed before the mosquito bites her waking her up, the camera shows the room with a circular movement and you can clearly see the window being dark, the only light comes from the lamps above the beds.

A screenshot of the window

This means that most of the hospital personnel is sleeping and that only those who have a night shift will be there at the hospital, one of them being Buck.

In the Kill Bill: Vol. 1 FAQ on imdb, there is a question that says "Are we really supposed to believe that she can stay in a dead guy's truck for 13 hours without the cops finding her?"

And the answer confirms what I said, also adding other theories (I added the numbers 1 and 2) and repeating what VoT said in his answer (emphasis mine):

No, just like we are not supposed to believe that arterial spray is that insane and that a very, very old Chinese man can stand on the tip of an outstretched sword (as happens in vol. 2). The film generally does not take a hard, realistic tone. It's possible that it could have been near the beginning of Buck's eight hour (or possibly longer) shift when The Bride took him out. Perhaps the next nurse coming in decided not to check on them for a while because s/he had other things to do, and no one found the bloody mess in the room for over thirteen hours. They were in the coma ward, where nurses possibly didn't check on the patients that often. By the time he was found, with all the usual shock of the discovery of a double homicide, it's entirely possible they didn't get around to checking his truck by the time the Bride left. (1) Not to mention, if they did check for his truck they would see that it was still there, and possibly wouldn't check inside. Seeing as how the truck wasn't stolen, they may not have found it necessary to check it. (2) The Bride also takes the keys to Buck's truck, and without those for identification, no one else might have known which car belonged to Buck.