I have not personally been here yet, but Initiative Outdoor runs a bouldering area at their location in Jhamsikhel. The cost for a day climb is RS 250 (including shoe and chalk bag) and there is no time limit. They are open from 10 am till 7 pm daily.
Like all thing in Kathmandu, giving directions is quite hard since very few streets have names. This place is south of the river. Please refer to the attached map or call them to get better directions.