Mussoorie to Harsil in January

I'd be visiting Uttarakhand in Jan second week with two friends. we are flying to Dehradun from our respective cities then heading to Rishikesh . 8-9 Jan : Rishikesh 10-11 Jan : Mussoorie 12-14 Jan : Harsil 15-16 Jan: Tehri Preferred most of commute between these places is shared taxi and bus. I am trying to figure out transport for sector Mussoorie to Harsil (via Uttarkashi) . I am not sure if there are buses or shared taxi from Mussoorie to Uttarkashi. The intel I recieved from internet was Dehradun to Uttarkashi @ 530 am and 1030 am bus, shared taxis between and after that, private buses too. ?? Any of these stop at Mussoorie? Are there cheap ways to commute to Uttarkashi from Mussoorie or we have to head to Dehradun for bus/shared taxis.Just want to get my head around this .....