I used one of those 'strap-ons'. They never fall off loose because it's strapped on with a rubber thingy that absorbs the vibration. It's a Zefal 'Spy Mirror' strap anywhere. The good thing about this is that you can strap it almost anywhere on your bike.
I found a mirror at Ace Hardware for about $8 that inserts into the end of the handlebar. It seems quite steady when riding. Although I have to adjust it every time I start out because I am always bumping it.
Why not buy a clutch mount from a motorcyle, from Ebay. Might be able to find one with mirror and lever complete. Just make sure it is for 7/8" not 1" bars.....Heres one from a Honda........
I just bought another mirror today ,found it at a schwinn shop so time will tell.
good Idea though the e bay thing. A motoecycle lever might be a bit of overkill but i was thinking that, probably would buy a new one if I decided on that.
The ones we use are from the motorcycle shop. They attach to the end of the bars and are tighten up with an allen wrench. They have never moved since I installed them. They aren't the cheapest ones. I paid $45 for two of them so I put one on my bike and Dean's.
I have a good quality clamp on mirror, to ensure it doesnt move put a small self tapping screw thru the clamp and into the handlebar, I also loctite this screw.
If you use a motorcycle mirror...may I suggest mirror dampers that take out 99% of the vibration.
They are around $10-15 and can be picked up at most motorcycle stores. I used a pair on my XR600 and even at 70mph bouncing, jumping through the desert my mirrors where nice and steady. On the street, they where absolutely perfect.