bus from Qingdao University to Mt. Laoshan

Yes, you can take route no. 304 to Mt. Laoshan Scenic Area.
About the transportation, there is no direct bus. You need to transfer to the Taiqing Palace.
You can take route no. 110 to Hejiacun Station. Then transfer to no. 106 to Yakou Station. After arriving, walk to the scenic area directly.

There's a new route 618 from Ya Kou to Yang Kou. Now 110 goes to Yang Kou and 304 only goes to Liu Qing He. 106 is from Licun to Yakou but there is only 4 times a day.