Last train is Haruka No. 47 departing Kyoto station at 8:15 p.m. arriving Kansai Airport at 9:43 p.m.
Last bus form Kyoto area leaves Keihan Sanzyo station at 9:06 p.m. and arriving at Kansai Airport Terminal 1 at 11:05 p.m. This bus originates at Keihan Sanzyo station but pick up passengers at few locations in Kyoto, including Kyoto station at 9:40 p.m. which I think is closest to Hyatt Regency Kyoto.