Just drive over and walk in the door, if they got the work and you got the savvy they will sign you on, good company's don't add drivers if there isn't enough work to keep the drivers already there busy. It might take a while before the hire you on.
Your looking for a courier service then not an expediting carrier. Best bet is see if you have a ceva office. They can be found near an airport. Mostly local work
Circled it on the calendar, 365 days from today I will enjoy my first day of retirement from expediting, that is as long as the crappy ford holds in there. Disclaimer: could be sooner might be later.