There is no direct connection from Dehradun to Shimla. However, you can take the taxi to Ponta then take the bus to Shimla ISBT Tutikandi. Alternatively, you can travel from Dehradun to Shimla in around 4 h 6 min.
How to get from Dehradun to Himachal Pradesh
From Dehradun taxi to Ponta then bus to Shimla ISBT Tutikandi. 6 h 47 min ₹1,422. From Dehradun taxi to Shimla. 4 h 6 min ₹3,171. From Dehradun drive to Shimla. 4 h 6 min ₹1,877.