Cyclists used to be able to bike between Lhasa and Nepal unimpeded. Prior to the 2008 protests it was possible to illegally cycle from Yunnan to Lhasa by crossing the border checkpoint during the pre-dawn hours. Since 2008 neither of these have been possible. I have spent months reasearching this topic online in preperation for my trip this summer, and have not discovered an account of independent bicycle touring within Tibet by foreign nationals since 2008. If you find such an account, let me know. Western Sichuan is also closed intermittently (as it is currently).
I do speak Chinese, but I don't see how that would help when I've been caught. Further, the three other cyclists I'm going with are all white, so we don't exactly blend in.