The public transit system in KC is pretty limited, especially after 6PM. Guest's sugguestion of taking the bus would work if you were arriving on a Weekday via the Eastbound SWC or the early MORR (Train #311)
However, if you are coming to KC on the Westbound SWC, on the late MORR (Train #313) or on any train on a weekend, the bus won't work for you.
The last bus to the airport (Bus 129 - I-29 Express) departs downtown at 6:02PM.
Since you stated you are arriving on the westbound SWC, a Taxi is going to be your best (and likely only) option. Generally, there are several taxis waiting for passengers in front of Union Station when the SWC arrives.... on the rare occasion that there are none, a quick walk to the opposite corner of Pershing and Main will take you to the Westin, where you would have no trouble getting a cab.