Kintetsu Limited Express operates a train from Asuka to Kyoto hourly. Tickets cost $14 - $19 and the journey takes 55 min.
How to get from Asuka to Kyoto
From Asuka taxi to Kashiharajingumae then train to Kyoto. 59 min ¥4161. From Asuka taxi to Kashiharajingumae, train to Takeda(Kyoto), then subway to Marutamachi. 1 h 29 min ¥3607. From Asuka taxi to Kyoto. 59 min ¥26787. From Asuka drive to Kyoto. 59 min ¥980.