Public transport (Large Land Cruisers - 18 passengers+1 or 2 goats or sheep and a few chickens) travel from Astore to Skardu (also from Gultari to Skardu) very early in the morning, it stops at Chilam but it is risky in case no one gets off at Chilam. Then they don't stop till the check-post at Skardu side at that end of Deosai. If you drop somewhere in Deosai they will charge full fare and the fare is high. In 2008, I paid Rs.300 from Kalapani (middle of Deosai) to Skardu, I think fare for Astore-Skardu was 600 or 650. If they don't have enough passengers they can postpone the trip for the next day. In my opinion you should try to join another group and hire a pickup, 10 or 12 people can travel on a pickup and you can stop at four or five usual points in Deosai.
Edit: The Land Cruisers don't leave from usual bus stand, they leave from their owner's shop or place of business, you will have to find it and book seats the previous evening. I have noticed that local people discourage tourists travelling on public transport and don't tell the location of these places easily. An owner may have only one vehicle so they travel on alternating days, one day Astore-Skardu and the next day Skardu-Astore.
