Personally, I wouldn't ride a bike with any glasses which have metallic frame (especially without flexible grips) and real glass lenses because of their weight and potentially sharp edges. I've seen a friend of mine who got pretty deep cuts on his nose after falling from a bike (wearing his expensive and heavy Police sunglasses which tore skin from his nose). (And after that injury he couldn't wear glasses for quite some time).
Since I needed both corrective lenses (myopia) and sun protection I've ordered custom tinted
plastic polycarbonate lenses and semi-rimless frame with flexible grips and that costed significantly less than some brand name sunglasses.
I could recommend above mentioned type of glasses (with or without prescription :). These glasses are quite light, flexible and can come off easily in case of falling. (Didn't fall with my glasses on so far, but I've dropped them numerous times and sat on them once - luckily no big damage).
I wanted to edit this question a long time ago because I've put the wrong term plastic were it should be polycarbonate.
As David Richerby mentions in his comment below, plastic is bad material for lenses due to fragmentation upon impact.
Here is a video which displays difference between plastic and polycarbonate lenses. Polycarbonate lenses won't shutter when impacted/stressed.
On the other hand, I would disagree about type of frames and whether semi-rimless or rimless frames are durable enough.
Another video of testing a sport performance product - a semi-rimless glasses from well known manfuacturer.