So you want to import the road markings or similar of the the cycle route from google into AutoCAD?
I'm pretty sure this is not possible. I've done many many TTM (temporary traffic management) drawings and I used google maps to view the road markings, but I always had to draw them manually (or create blocks for certain things like directional arrows).
However, I think http://www.promap.co.uk/ can supply UK OS maps for use in AutoCAD which contain road markings. Not sure how much they cost but if I remember correctly, you can pay for them by a user defined area (instead of 1km tiles), so, depending on the size of your project, and if it is based in the UK, the site might be worth looking at.