It's never the end of the stick that makes contact, that's just gonna hurt. The first inch of the stick next to the chain or chord is the important bit. In the diagram I've hopefully attached you'll see how the chuck lies in a bounce. Try it with the chuck laid across your outheld arm like in the diagram. Note that when you pull on the stick you're holding it'll 'flick' the other one up as the chord/chain comes taut. There' very little energy transferred into your arm (or whatever else you're bouncing on) like this.
As regards specifics for the shoulder bounce, I find it works best on the pad of muscle that joins your arm and shoulders, gives you a bit of padding if you misjudge it a little as well. Most people would distinguish between side and hips bounces with side bounces being on the ribs under the armpit and hip bounces being (you guessed it) on the hip.
Bounces are subtle, and take a while to become second nature, work on getting them smooth, with as little force transferred to the body as possible.

EDIT: Now with added YouTube vid.