Most people come by bus via Rampur, although also accessible via Kaza. The bus journey from Rampur to Reckong Peo has to be one of the most dramatic in the world, definitely not for the faint hearted. As of summer 2015, the cost from Rampur to Reckong Peo was 178INR.
In summer the night busses from Shimla are hopelessly overcrowded; so, very early morning busses are more spacious. Direct busses are not necessary; in fact, in summer it's better to take anything to Rampur, and go from there. The few semi-deluxe busses start in Chandigarh, and are generally full in summer before they reach Shimla.