Thinking of getting bus from Dongzhimen to Mutianyu. We will have backpacks.

No, generally speaking, there is no problem. From Dongzhimen, you can take bus line 916 Express to Huairou North Avenue Bus Stop. Then transfer to bus line h23, h24, h35, or h36 to Mutianyu Roundabout. walk around 50 meters to the ticket office of the scenic area.

Thanks Carter. I was thinking about the crowds on the bus and lugging a large backpack into a sardine-packed bus full of Chinese locals. Also if bus driver might not allow it.

Generally speaking, you don't need to worry about this problem. You are allowed to bring the luggage on the bus.