Is there a bus that goes from Mudanjiang to Jingpo Hu?

Yes, there are. At MDJ General Bus Station, two buses are scheduled daily to Jingbo Lake at 13:35 and 14:30. It costs CNY20.5 per person.

I also heard that from June to Oct. a direct bus is arranged leaving from the square of the south exit of MDJ Train Station at 08:00 and getting back at 16:00. The bus fare is CNY30 per person!