"Bye, Charlotte, thanks for staying late."

Charlotte gave an acknowledging wave over her shoulder as she stepped out the door of the Cajun Blues Bar and Grill. The screen door shut behind her with a loud bang. She had left the hazy interior behind, but the odor of fried food clung to her nostrils and clothes. She couldn't wait to get home and take a long, hot shower to clean the grease off.

Gravel crunched underneath her feet as Charlotte crossed the parking lot to her car. She nervously eyed the lot next door. It was empty of buildings, but live oak dominated the small patch of land. There were a few scattered lights in the parking lot, but shadows still clung to the trees,

There's potential in this opening, with Charlotte spooked by the empty lot. Definitely leaves me wondering what's going to happen next.

I'm not convinced however that starting with dialogue from an unnamed, unseen and quite probably unimportant character is the way to go. It might work better to start with Charlotte acknowledging x's implied remark with a wave of her hand. You can easily use narrative to tell the reader how late it is, which is all we really get from the dialogue.

Having the gravel crunch underneath Charlotte's feet feels tautologous--where else is it going to be?

Try to avoid having two consecutive sentences that use the same construction. Here you have two very similar sentences using "but". Rhythm is often overlooked by prose writers, but it is important. Vary the lengths of your lines and how they are constructed.