Having lived in Lancaster and Ridgecrest...
Your first two concerns would be WIND and HEAT, then pavement and bike lanes.
The west wind is pretty steady. Mojave is just down the hill from the Tehachapi windmill farm. Gusts can be really impressive. On rare occasions they shut down the highway so the toy haulers don't blow over (and wrecked toy haulers are a pretty common sight on weekends). This also means sometimes there are dust storms. It's a desert, with temperature often going over 100 F in the summer, but in the winter it's pretty nice. Rain is very rare, coming in a few big storms each year. The air is very dry.
CA-14 is a freeway with overpasses. I don't recall but I doubt bikes are allowed. Sierra Highway, which runs along the railroad tracks parallel, is 2-lane blacktop, and is paved the whole way. There's a grid of surface streets more or less the whole way that you'd probably want to take. Most of them turn to dirt north of Rosamond, which means sand and washboards.
I don't recall any of these roads having bike lanes. Shoulders are deep and gravely. It looks like Sierra Highway has a fog line south of Rosamond, but not north. Traffic will be usually thin on the surface streets because they parallel a freeway, but anyone on them will be going 60-70 mph.
Edit: I can see on Google Street View at the Rosamond entrance to 14,
PEDESTRIANS
BICYCLES
MOTOR-DRIVEN
CYCLES
PROHIBITED
Another edit: here's a page showing weather for the last year
Weather History for Mojave, CA | Weather Underground