The JR bus "Dream" bus services leave from Tokyo and Shinjuku stations.	The Keihan Bus "Kyoto" bus services 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 ¥8180, to Osaka ¥8610 and to Nara ¥8400.
 Furthermore, if you have the Japan Rail Pass, your pass is acceptable and valid on the following JR "Dream" bus services. The Dream Nagoya service between Tokyo and Nagoya, the Dream Kyoto service between Tokyo and Kyoto, and the Dream Osaka service between Tokyo and 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 ¥8180 (¥8100 for the "Dream" services) and the round-trip discount fare is ¥14400.

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 ¥14190 for Nozomi, and ¥13220 for Hikari.

Flying to Itami or Kansai Airports takes 60 minutes; the one-way fare is ¥16250 (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 services operating between both cities; the JR Bus Kanto company (Tel.03-3844-0495: open hours 10am to 6pm) and Nishinihon JR Bus (Tel.06-6371-0555: open hours 8am to 9pm) operate two "Dream" services a day from Tokyo Station (Yaesu South Exit) and Shinjuku Station (New South Exit);

The Keihan Bus company (Tel.075-661-8200: open hours 9am to 7pm) operates the "Kyoto" services from Shinjuku Express Bus Terminal, Shibuya Mark City and Keisei Ueno Station. Reservation on Tokyo side is accepted by the Kanto Bus company (Tel.03-3928-6011: open hours 9am to 7pm) from Shinjuku and Shibuya, and Chiba Chuo Bus (Tel.047-432-1891: open hours 10am to 7pm, until 6pm on Sundays and Public Holidays) from Ueno.

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

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

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

The features of each service are:

The "Dream" service accept reservations by telephone from a month before travel. They use a double-decker bus (39 seats). The bus stops twice at service areas on the expressway, where you can buy drinks and food. You can buy a ticket at major JR Stations "Midori no madoguchi" or ticket windows. However, passenger services are limited to blankets, slippers and a toilet. In addition, you can get discount tickets for bathing at Shinjuku or Kyoto, and for bathing and breakfast at Tokyo. Students are able to apply for a special one-way discount. The discount fare is ¥6480.

The "Kyoto" services accept reservations by telephone from a month before travel. They use a high-decker bus (29 seats) and 10 rows of 2 pair seats for the Ueno ‹–› Kyoto service. Note that this service doesn't have a stop for passengers, only for a driver changeover. Services are similar to the Dream bus service, but also serve hot and cold water. Students are able to apply for special round trip discounts. The discount fare is ¥12500.

The "Flying Liner" service accepts reservations by telephone from a month before travel. They use a super high-decker bus (28 seats). Note that this service doesn't have a stop for passengers, only for a driver changeover. Services are similar to the Dream bus service, but also serve hot and cold water, and Japanese tea. In addition, the Kintetsu Bus service serves coffee and juice. Students are able to apply for a special one-way discount. The discount fare is ¥6540. It is available from October 1.

The Ikebukuro, Shinagawa ‹–› Kyoto, Osaka service accepts reservations by telephone from a month before travel. They use a super high-decker bus (29 seats). The bus stops twice at service areas on the expressway, where you can buy drinks and food. Services are similar to the Dream bus service, but also serve hot and cold water, and Japanese tea. Students are able to apply for a special one-way discount. The discount fare is ¥6540.

The "Southern Cross" service accepts reservations by telephone from a month before travel. They use a high-decker bus (29 seats). Note that this service doesn't have a stop for passengers, only for a driver changeover. Services are similar to the Dream bus service, but also serve hot and cold water, Japanese tea, and coffee. The fare between Akihabara Station and Kyoto Station is ¥6500 one-way and ¥12400 round-trip.

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