I had to make an unexpected trip to the airport today, thought I would offer this:
Taxi: From the arrivals hall exit door to the door of the K+K Hotel not more than 45 minutes with average wait time for the taxi, and 10.000 ft. Includes 1 minute of walking to the taxi kiosk.
100E Bus: From the arrivals hall exit door to the door of the K+K Hotel including a short trip on the M1 Metro not more than 60 minutes with average wait time on the bus and the metro, 2.200 ft (free if 65 or older) for the 100E the M1 free with a Travel Card. Includes 3 minutes of walking at each end (6 total). You often have to stand the whole way.
200Bus: From the arrivals hall to the Kőbánya-Kispest M3 Metro Station to the Deak Ferenc ter M1/M3 Metro Station to the Opera M1 Metro Station to the K+K hotel not more than 1:15 with average wait time on the bus and the metro. Free with TravelCard. Includes 3 minutes of walking at each end and from the 200 Bus to the M3 (9 total). You often have to stand the whole way.
So add those times on to the 2 hour pre flight arrival time. 90 minutes is enogh but 2 hours gives you time for accidents, traffic issues, etc.