You CAN take Amtrak from Colorado Springs, CO to Las Vegas, Nevada for about the same price as a Greyhound-all-the-way bus trip (trust me, you do NOT really want to do the all Greyhound thing).
Here's what you would do. If you go to
amtrak.com and type in COS (Colorado Springs) as your starting point and LVS (Las Vegas, NV) as your destination the system will route you correctly via Denver and Salt Lake City.
You will start by boarding a thruway motorcoach at 5:00am in Colorado Springs for a short, pleasant ride to the train station in Denver. The motorcoach will arrive in Denver at 6:25am and you will then transfer to Amtrak train 5, the westbound California Zephyr (departs Denver at 8:05am), for a scenic train ride through the Rocky Mountains with gorgeous scenery unlike any other. You will arrive into Salt Lake City, Utah at approximately 11:33pm that night, probably a couple hours late since this train tends to run late. You can hang out at the train station until 5:30am (they will remain open waiting for another train and other passengers will be there). The Amtrak agent will then give you a voucher for a free taxi ride over to the Greyhound bus station where you will board an Amtrak/Greyhound Thruway Motorcoach at 8:30am to complete your journey into Las Vegas, Nevada. The bus usually isn't crowded on this portion of the route so you should have adequate room to stretch out and sleep if you wish or just enjoy some scenery. The coach should get you into Las Vegas, NV around 3:30pm which will be perfect if you are checking into a hotel there. The bus station in Las Vegas is downtown adjacent to the Fremont Street Experience.
Amtrak offers a similar, coordinated schedule for return from Las Vegas, NV to Colorado Springs, CO if you need to take advantage of it. You can book the entire trip online at Amtrak's website or through your local travel agent and Amtrak will issue tickets for all portions of the trip: train and connecting buses. You
could fly, I suppose, for a faster trip, but it would be a little more expensive and you would really miss out on some of the very best scenery the U.S. has to offer. If you do the train/bus combination you won't be disappointed when it comes to the scenery.