Ideally it would be great if you had a padded bag that was pretty light and the camera could be accessed easily. I got one of these for $30 -
I cut off the padded belt which saved weight and increased internal space (I didn't need to carry the middle portion of the belt).

That being said, I must admit I stuff it with my wallet, cell phone, a bandanna, an extra sweat band, sun tan lotion, extra bags of my DIY sports drink powder, a power bar, and a PB&J sandwich, and now I don't have space for my camera. [I'm so fat I don't wear a cycling jersey - it seems to me like it would be an affront to sensibilities everywhere!]