score:15
Here is a link to a good site that compares costs and times of different modes of travel between different places. It doesn't always know about every single special offer, but it's very good at giving a general view of pricing and time.
As you can see, in your case (and not considering dates)
Upvote:1
While a cross-country Amtrak trip is on my bucket list, taking a train is not going to be your cheapest travel option, in terms of time and money. The train is going to take literal days each way, and is going to cost a few hundred. If you then add on the cost of meals on the train, you're looking at another hundred. I'm sure a bus is going to be about the same, but it will be extremely uncomfortable and miserable.
In this current economy, and with your itinerary, flying is going to be your cheapest option. If you want prices and specifics you can try that really cool website @DJClayworth linked, or flights.google.com for flight prices and whatnot.