I found that the Sony NEX-5 with the 16mm lens (24mm equivalent) worked well for self portraits while cycling, but the angle of view is too wide for most scenics from a bike, resulting in 70% pavement and 30% scenery. A 35mm - 50mm lens (in full frame terms) is better for such things, with a 35mm still usable for self portraits.
I let my beard grow while traveling in the high country to help reduce sun exposure (and it’s nice not to have to shave)!
With Leica M lenses
Using an adapter, Leica M lenses can be used, as here, with the Leica 35mm f/1.4 Summilux-M ASPH. A zoom-feature with Live View makes precise focus quite usable, with the downside of a difficult to see screen under some lighting conditions.