She barely had time to catch that he might have just flirted with her- a vampire- before he started turning all over the place. The entire time, she clung onto the sides of her seat, stiff as a board. if she still had some color as a living individual, she might have blanched. 

What was chasing them was a grey SUV, and it appeared to be full of people. What was ALSO chasing them was a police car. no doubt because of Connor's crazy driving. At this point, elizabeth just shut her eyes. Why was this happening to her? Not only would she have the entire town's population of vampires on her tail, but she's teamed up with a vampire hunter who had previously wanted to kill her, and his crazy driving was going to have all the cops on them. 

And, to top it all off, he barked an order which made her uncomfortable while turning so sharply, she almost flopped onto his lap. Still, she managed to reach over and retrieve the gun for him, catching herself praying that this this was done soon.