Which bus line to catch to explore beach side at Mount Laoshan?

Yeah, you can take bus 106 to the beach area. You can take the bus from Yakou in Laoshan Scenic Area (near Taiqing cable car) to Yangkou, and then walk to the northeast for about 400 yards to reach the Yangkou Beach. Or you may need to rent a car to go. You can swmming in the bathing beach there.
By hanging bridge I’m not sure whether you mean Zhan Bridge. If yes, there are lots of buses available, such as nos. 6, 8, 25, 26, 304, 305, and 321. You should get off at Zhanqiao stop and then walk south to reach the bridge.

Routes 104 and 304 both serivce the Tourist Service Area on the ocean side of Mt Lao. From the service area, you can choose which sights you wish to visit. The Beach and Buddhist temple side also has a village with restaurants and a waterfall and reservoir. The trip to the top of the mountain is a separate choice but is also serviced by the Tourist Service Center bus. Buses 104 and 304 are running east and west on Hong Kong Road when they pass through the downtown area. ( May 4th Square, Olympic Sailing Center, Aeon and Carrefour Market areas.) They continue on Hong Kong road past Laoshan when the road's name changes to Shandong Road. The entrance to the Tourist Service Area are clearly marked. When exiting the Laoshan Scenic Area, the first stop (before you stop at the Tourist Service Area is a small village where there is a Bus 104 stop. Taking this stop will often return you to the city quicker than the Tourist Service Area bus choices and because it's the turn-around point for the bus route, you are almost guranteed a seat on the bus, rather than a standing position.) It's a great area, enjoy!