From Kansai- airport,you can take the bus,train and a taxi.
We recommend MK Sky Shuttle to you. It is a taxi that the person who goes in the same direction get in together.MK is a famous company in Kyoto with respectful service.
However,you have to make reservation 2 days before.
Please check the details the following site.
Mk sky gate shuttle
Of course, you can take it from the apartment to the airport , also .
When you would like to take a taxi in Kyoto,catch this crown's one,it is MK.