Take UTC bus from Rishikesh to rudraprayag and then fron there to chopta. They have some timmings for the buses u will know it from Rishikesh bus stand and travel in day time.
Ur route is correct... from rishikesh to rudraprayag u will get gmou buses from bus stand, buses start early morning from 3.30 am then, rudraprayag to ukhimath by shared cab/buses then from ukhimath to chopta u will have to hire a cab or u might get the shared cab depends on the number of tourists available.