It is relatively easy and cheap to visit the Burana Tower from Bishkek by public transport. First you will need to find a cab to bring you to the Western Bus Station in Bishkek. From the Ala-Too Square it will take approximately 8 minutes by cab. Meanwhile, by foot you should count on 38 minutes. 

At the busstation head towards the Marshrutkas towards the town Tokmok. since it is a popular route, make sure to get in front of the queue, people tend to push and jump the queue when the bus arrives. The transportation time is about 1,5 hours. When you arrive in Tokmok, make sure to grab a cab to the Burana Tower which is located only 10 minutes from the busstation. Ask your cab driver to wait at the gate of the Tower, since there are no other taxis or public transport to bring you back to the busstation.