Cedar City is near ST George, I know you can get shuttles to Las Vegas from there.
Carson City is near Reno.
Reno and Vegas both are served by Southwest Airlines, which has a reasonable bike-handling fee.
There may be other factors at play here beyond the knees that make you want to break the trip up, but IMO doing that adds a huge amount of time and expense for travel, that might be otherwise spent touring. You might even do a cost analysis to see if a hotel-based trip would break even, and maybe spare the knees the pain of pushing camping gear up hill? Or maybe you could just do 4-days on, 2 days off? I don't know the rest of your constraints, of course.
The bus is so horrible and time consuming. It might not even be all that cheap. Greyhound's web site should show you the bus service info, better than asking here. Don't count on finding a bike box at the station, even if they say they have them.
Good luck! I'm sure you can figure it out.