Express bus="Kousoku basu(高速バス)" in Japanese.
Duration: 2hours (toilet, free wifi are available on the bus)
Fare(one way):
From Kyoto station to Miyazu(宮津): 2600yen
From Kyoto station to Amanohashidate(天橋立): 2800yen
You can reserve your seat from 1 month before of the departure day. I personally recommend to book your seat in advance.
If you are already in Kyoto city, you can buy the ticket at "Bus ticket centre(バスチケットセンター)" which located in front of Kyoto station, besides bus terminal.
You can also reserve your seat by calling this number 0772-42-0338, if you calling from foreign phone +81 772 42 0338. (perhaps they can't speak English.....)
Possible to pay by cash on board but make sure you have exact money.
***You can also book your seat online in English now : D (Updated on 28th July 2016) Select your origin point as "Kyoto" and destination point as "Kyoto" and the bus route will be appear.
https://willerexpress.com/en/
Each seat has number and driver will tell you before you get on the bus so please make sure to sit on the correct number seat. When you get on the bus, you need to show your printed out ticket or smartphone(iphone) screen of your booking to the driver. Your ticket will be send to your email address when you make a reservation.
Time schedule (Everyday)(Last updated on 26th Mar. 2017)
From Kyoto station to Miyazu station/Amanohashidate station
8:55→10:51/11:00
12:40→14:36/14:46
18:00→19:56/20:03
From Amanohashidate station/Miyazu station to Kyoto station
7:18/7:27→9:30
12:58/13:07→15:08
17:05/17:14→19:15
For April&May 2017, there will be one extra bus available, for further information please read another page of my blog. http://seasidekyoto.blogspot.com/2017/03/express-bus-to-amanohashidate-and-ine.html