The bus is, hands down, the cheapest way, on either route. On advance tickets, you can cross the entire continent on Greyhound for about $150. Of course, you can't forget that you'll need to feed yourself during that 3-4 day journey, so that will add a bit to the cost. Both Amtrak and VIA
Rail are likely to be cheaper in coach than most flights would be, as well, but again you'd need to add the food. As for air, well, you know how to use Expedia, no doubt!
Next flight.... who knows.