Cheapest way to get from Tucson, AZ to Boulder, CO?

As others have mentioned flying can be equally cheap as taking the bus or train on a journey of this length, depending on the time of booking, and if you're traveling round-trip. Driving is likely a bit more expensive if you don't already have a car.

If you are traveling last-minute or one-way bus seems to be the best way. For that it'll be easiest to travel from Tucson to Denver and then connect onward via local public transportation to Boulder. Here's the public transportation schedule from Denver to Boulder http://www3.rtd-denver.com/schedules/getSchedule.action?routeId=AB

It's not easy to find bus companies in the US, though rome2rio can be very useful. At Busbud.com we're working on a search engine for this. We're not covering Tucson - Denver just yet, but I know that in addition to Greyhound, EP LA Limo has connections which are a bit quicker than Greyhound and also cost around $100 one-way.

Given your scheduling, one option is to drive. Google Maps shows it as a 13 to 13.5 hour drive, all on major highways (i.e. no questionable remote back roads involved). Both Orbitz and Expedia suggest that a one-way car rental from Tucson would cost about $145 including fees. Of course, with a drive that long you might want to stay overnight on the way. That would raise the cost but it would still be possible to arrive within the rough day and a half window you mention.

On Greyhound I can find one way tickets from Tucson to Denver for 99$. It takes less than 24 hours and has a transfer in Las Cruces, New Mexico.

Boulder is in the Denver metropolitan area, so transfer from Denver to Boulder is trivial.

I doubt any other mode of transportation is going to systematically beat that, although you may or may not find cheaper airfares — flight fares are often harder to predict than bus fares, and may have more additional fees for luggage and perhaps other things, so you should check both options for your specific travel dates, and be sure to check in detail all additional fees that will apply to you in either case.

In general, to find travel between any pair of cities, I start with Rome2rio, then look at bus and train options, which in the USA can be either Greyhound, Megabus, Amtrak, or flights. It very much depends on the location — right now I'm in a small town in the Mid-Western United States, and it's cheaper to sit 24 hour on a bus than to fly anywhere from the local airport — and for the price to get to the local airport in the first place, I can easily make the 5-hour bus ride to the nearest international airport...

I am guessing you are searching for flights from Tucson (TUS) to Denver (DEN), but you can get much cheaper flights from Phoenix (PHX). I'm seeing round-trip fares PHX-DEN-PHX of $112 (Spirit Airlines, many extra fees likely), $144 (Southwest, includes bags) and $185 (US Airways, bags extra). The difference would probably cover a shuttle from Tucson to PHX (or you may be able to arrange a rideshare even cheaper).

Note that Southwest Airlines is a big player in this market (PHX and DEN are both big Southwest hubs and they run 9-10 nonstops per day), but they don't list their fares on the major travel sites (Orbitz, Kayak, etc). You have to go to Southwest's own site to see their fares. In this case it's worth doing.

Southwest will also sell you a nonstop TUS-DEN-TUS for $244 round trip.

To get from the Denver airport to Boulder, check out the public Skyride bus for which the fare is $13 each way.

Edit: If you are only traveling one-way, don't despair. On most US domestic flights these days, a round-trip fare is about the same as two one-way fares, so for each of the fares above, you should be able to get a one-way for about half the price. (It used to be that two one-way fares were far more expensive, or that round-trips required a Saturday overnight or some such, but those phenomena have mostly vanished.)