I plan to go to Las Vegas next summer. Checking Amtrak, a 1 way trip* would be $470, take 76 1/2 hours and consist of:
4:35 bus trip from Houston to Longview, TX
15:40 train trip to Springfield, IL
2:15 bus trip to Galesburg, IL
31:27 train trip to Salt Lake City, UT
8:05 bus trip to Las Vegas.
plus lots of layover time at each connection.
* round trip fails to find a route