The JR bus "Dream" routes leave from Tokyo and Shinjuku stations.	The Keihan Bus "Kyoto" routes depart from Tokyo Shinjuku/ Shibuya and Ueno.

Overnight buses are the cheapest way to travel around compared to other means of transport.
This also saves the money for a night’s accomodation. Leave the place of origin at about 6pm to 11pm, and arrive at the destination the next morning around 5am to 8am.
 For example, the one-way cost from Tokyo to Kyoto is ¥8,180, to Osaka ¥8,610 and to Nara ¥8,400.
 Furthermore, if you have the Japan Rail Pass, your pass is acceptable and valid on the following JR "Dream" bus services. The Dream Nagoya route (Tokyo to Nagoya), the Dream Kyoto route (Tokyo to Kyoto) and the Dream Osaka route (Tokyo to Osaka).

These buses are generally for reserved seats only, although some seats may be available without a reservation. Additional buses exist in busy seasons.

Comparison of costs and required times of travel to Kyoto from Tokyo by bus and other means of transport.
Buses take 8 hours; the one-way fare is ¥8,180 (A round-trip is ¥14,400).

The Shinkansen or bullet train is the choice for the majority of travelers.
Bullet trains are extremely fast and comfortable. It takes 2 hours and 15 minutes by the fastest "Nozomi" and 2 hours and 40 minutes by the "Hikari"; the one-way fare is ¥14,190 (Nozomi), ¥13,220 (Hikari).

Flying to Itami or Kansai Airports takes 60 minutes; the one-way fare is ¥16,250 (Normal fare doesn’t include the transport between airports and the city).
Note that Kyoto itself doesn't have an airport, so a connection is required. This will take 55 minutes from Itami by bus; 75 minutes from Kansai by JR limited express train "Haruka".

There are six routes running between both cities; the JR bus (Tel. 03-3844-0495: open hours 10am to 6pm or 06- 6371- 0555: open hours 8am to 9pm) run two "Dream" services a day from Tokyo Station (Yaesu South Exit) and Shinjuku Station (New South Exit);

The Keihan bus (Tel. 075- 661- 8200: open hours 9am to 7pm) runs the "Kyoto" routes from Shinjuku Station West Exit Expressway Bus Terminal, Shibuya Mark City and Keisei Ueno Station. Important notice: From May 11, the route from Keisei Ueno Station only runs between Thursdays to Sundays for the Down bus and Fridays to Mondays for the Up bus. And the bus also runs on addtional days of August, September, November and December.

The Tohoku Express Bus (Tel. 03-3529-0321: open hours 9am to 7:30pm) and the Kintetsu Bus (Tel. 06-6772-1631: open hours 9am to 7pm) run "Flying Liner" route from Tokyo Station Yaesu-dori (Nichido Building).

The The Hankyu Bus (Tel. 06-6866-3147: open hours 8am to 7pm) run the Ikebukuro/ Shinagawa to Kyoto/ Osaka route from Ikebukuro Station East Exit and Shinagawa Bus Terminal. Reservation on Tokyo side is accepted by the Seibu Bus (Tel. 03-5910-2525: open hours 9:30am to 8pm and the Keihin Kyuko Bus (Tel. 03-3743-0022: open hours 10am to 5pm).

The Chiba Kotsu (Tel. 0479-22-8577: open hours 9am to 6pm) and the Nankai Bus (Tel. 06-6643-1007: open hours 9am to 10pm) run "Southern Cross" route Akihabara Station and Narita Airport.

The features of each route are:

The JR bus "Dream" routes accept reservations by telephone from a month before travel and use a double-decker bus (39 seats), and takes a rest twice at service areas on the expressway.
You can buy a ticket at major JR Stations "Midori no madoguchi" or ticket windows. However, passenger services are omitted except blankets, slippers and a rest room.
The bus takes a rest twice at the service areas on the expressway; you can supply drinks and food there.
In addition, you can get discount tickets for bathing at Shinjuku or Kyoto, for bathing and breakfast at Tokyo. Note that a round-trip fare is not available.

The Keihan bus "Kyoto" routes accept reservations by telephone from a month before travel and use a high-decker bus (29 seats) and 4 seats per row for the Ueno to Kyoto route. Note that this route doesn't have a passenger's rest and only has for the driver's alternation. Services are similar to the JR bus, but also serve hot and cold water.
Students are able to apply for special round trip discounts. The fare is ¥12,500.

The "Flying Liner" route accepts reservations by telephone from a month before travel and use a super high-decker bus (28 seats). Note that this route doesn't have a passenger's rest and only has for the driver's alternation. Services are similar to the JR bus, but also serve hot and cold water, Japanese tea. And the operation of the Kintetsu Bus service serves coffee and juice.

The Ikebukuro/ Shinagawa to Kyoto/ Osaka route accepts reservations by telephone from a month before travel and use a super high-decker bus (29 seats). The bus takes a rest twice at the service areas on the expressway. Services are similar to the JR bus, but also serve hot and cold water and Japanese tea. Students are able to apply for a special one-way discount. The fare is ¥6,540.

The Nankai bus "Southern Cross" route accepts reservations by telephone from a month before travel and use a high-decker bus (29 seats). Note that this route doesn't have a passenger's rest and only has for the driver's alternation. Services are similar to the JR bus, but also serve hot and cold water, Japanese tea and coffee. Students are able to apply for 20% off one-way discounts.

In Kyoto, the stop for the JR bus and the Ikebukuro/ Shinagawa to Osaka are at Chuo (Central) Exit (the Ikebukuro/ Shinagawa to Osaka route is New Hankyu Hotel) is located in front of the Kyoto tower. The Keihan bus, the "Flying Liner" route and the "Southern Cross" route arrive at Hotel Keihan Kyoto of Hachijo (Shinkansen) Exit (the "Flying Liner" route and the "Southern Cross" route are Shin Miyako Hotel), located the opposite side of the Chuo Exit.
I recommend you get off at Chuo Exit to take the city buses or subway and JR lines. These stops are very close.