Adam, when you exit baggage claim thru the doors that say "shuttle"
Just walk to one of the booths & ask when their next shuttle to DT is?
Often they have other stops Before heading DT. So Ask First.
If it sounds like too long? Walk to the other shuttle booth.
Don't PAY Fare, until you find one that is leaving soonest for you.
Also, pay only One way. Don't buy roundtrip. They are notorius for forgetting you
or being late on returns. Get your Return tix at your hotel, or take taxi for return.