The FAQ puts the park on Yas Island, 50 minutes from Dubai, and the visitor page says about 50 minutes' drive. The visitor page itself gives two airport times, 10 minutes in its Location tab and 15 minutes in its Island paragraph, and the FAQ says 15, so we promise none of them. Parking in the Grand Prix car park at Yas Mall is free during your visit, with proof of entry on request; valet parking is AED 52, and VIP valet AED 100.
Both parks' FAQs say return buses run daily from Dubai for ticket holders, and link a Yas Express timetable. Pages 36 and 37 of that booklet, headed Bus Arrival Timings, show the Dubai routes running by day, not daily from every pick-up. The booklet carries no validity date, so confirm the current timetable with Yas Express before you travel. Al Barsha (Route D1), Mondays, Wednesdays, Fridays and Sundays: Mercure Barsha Heights 09:20, then the Warner Bros. World stop (shared with Yas Waterworld) 10:50 and Ferrari World 11:10; the evening bus is at the Warner Bros. World stop at 19:40 and Ferrari World at 20:00, and reaches the Mercure at 21:30. Dubai Marina (Route D2), Tuesdays, Thursdays and Saturdays: Millennium Place Marina 09:20, Warner Bros. World 10:50, Ferrari World 11:10; evening Warner Bros. World 19:40, Ferrari World 20:00, back at 21:30. Deira City Centre (Route D3), Thursdays and Fridays: Colors Café 11:00, Ferrari World 12:55, Warner Bros. World 13:05; evening Warner Bros. World 19:40, Ferrari World 19:50, back at 21:45. Sheikh Zayed (Route D4), Sundays: H Hotel 09:30, Ferrari World 11:40, Warner Bros. World 11:50; evening Warner Bros. World 19:40, Ferrari World 20:00, back at the H Hotel 21:30. Dubai Marina JBR (Route D5), Saturdays: JA Ocean View JBR 11:00, Ferrari World 12:40, Warner Bros. World 13:00; evening Ferrari World 19:40, Warner Bros. World 20:00, back at 21:30. The park pages add that the service is free, that you must show a valid e-ticket and be at the stop 5 minutes before the bus, and that times are approximate because of traffic.