I calculated this series of waypoint-to-waypoint distances using this website tool. It calculates straight-line distances based on latitude and longitude, as well as from a pretty comprehensive placename database.

I haven't checked these figures; I assume they're accurate. They are, of course, crow-flies distances. I'm reckoning on actually cycling distances being up to 2 times further, to account for detours, road wiggliness, switchbacks, getting lost, etc. Note also that the route given here is one potential route (in effect the "Trans-Manchurian", rather than the "Trans-Mongolian"), not necessarily the route I will actually take.