There is a bus from Hong Kong Heritage Museum going to Chungking Mansion?

Yes, take bus no.81C at Che Kung Miu, get off at Middle Road Tsim Sha Tsui. Then walk northeast around 80 yards (70 meters) to find the destination.
The normal ticket fare is 7.8 HKD per person. But I cannot find the exact discounts. Maybe you can ask help for the staff at bus station. :)