I just replaced the RHS mirror on my 85 K100RS a few weeks ago. The mirror came with a unique spring clamp in the box. It's actually a fairly clever design. You put the mirror in the socket, then install the clamp from the back side.
The mirror has a ball end with a groove machined into it. The c-clamp is about 3.5" long, and is made of spring wire about the thickness of a paper clip. One end of the clamp has a c-shaped bend that fits around the machined groove on the mirror ball and the other end is formed into a handle, sorta like a tongue depressor or popsicle stick shape (but of wire of course).
If you remove the turn signal assembly from the bike, remove the turn signal lens from the mirror and then as you insert the new mirror glass you can actually see the ball inside the housing as you look thru the back side. I may have had to remove the bulb -I'm not sure. I think I was able to get the housing to separate once I had the bulb out. I had to fiddle with it a bit but once I could see the ball I figured it out.
Anyway, you just grip the handle end of the clamp, press it into the opening in the back side of the housing where you can see the ball inside and it locks the mirror in place. The clamp and handle are all one unit so that if you ever have to remove it again you can just tug on the handle and it comes loose.
I'm assuming you ordered a new mirror glass directly from the BMW dealer. It should have been in the box with the mirror and may have been loose in the bottom. Hopefully this helps.