Although the holy Bagmati River looks dirty and polluted in Kathmandu, at its source it is pure, emerging as a spring in the Shivapuri Hills north of the city. You can hike in the Shivapuri National Park to this sacred Hindu pilgrimage site.
Making an early start, you can catch a Sakya bus or microbus no 5 from the centre of Kathmandu to Budhanilkanath and walk up about 30 minutes to the Shivapuri Nagarjun National Park entrance that is uphill from the sleeping Vishnu in Budhanilkantha, which is also well worth a visit. The Park opens at 7am and closes at 5pm.
It talks about three hours to reach Baghdwar, passing the Nagi Gompa monastery on the way. The first hour is along a dusty trail and then you take the stone steps up towards Nagi Gomba, a Tibetan nunnery. There are good views from here of the city and the mountains to the north.
To continue to Baghdwar or the summit of Shivapuri you follow the stone steps from the back of the nunnery for another two hours. As you go up it gets greener and you walk through thick forest (the area is very good for birdwatching). The sourse of the Bagmati comes out as a small spring at Bagdhwar and is surrounded by cool mossy trees. There is a sacred water tank with a Shiva statue in the middle, with a number of small temples and many statues decorated with red and yellow tikka by the many Hindu devotees who come here.
Continuing up for another hour brings you to the summit of Shivapuri. You can then walk down to Sunderijhal where there are plenty of buses back to the centre of Kathmandu.