I talked to someone at our hotel this morning about transportation to/from the airport. There is not complimentary hotel shuttle. Your best bet is a taxi which has a fixed rate of $36 for the first two people and $15 per person after that. They do have Uber and Lyft, but you might hit surge pricing when you get there, so your mileage (and cost) may vary. There is a hotel shuttle that goes to/from the airport and travels the circuit of hotels for $25 per person. But know that it will stop at ALL of the hotels, so it could take you a while to get to the Drury.
I hope that helps.