14 days in Spain

Gayle....depending on your likes and dislikes, the cities you 'must' go to don't necessarily adhere to seeing 'the best parts of Spain as possible.'
If you must do the cities and towns you list because of some sort of commitments (visiting family or friends), then I would suggest Madrid-Cuenca-Valencia-Barcelona.
There are about 8 buses/day from Madrid to Cuenca, taking about 2.5 hours for 14 Euro. Click here to check them.
From Cuenca to Valencia is a little more problematic. You may have to back-track all the way to Madrid to make any sort of connection. The alternative would be to catch the train at Cuenca for Valencia. Click here for the schedules from RENFE, the national rail service. It's in Spanish, but you should be able to figure it out. There are four trains/day and the cost is only 13 Euro per person.
From Valencia to Barcelona, there are several buses/day. The trip is 4 to 4.5 hours, and tickets are around 25 or 30 Euro, depending on whether you take a slow or fast bus.
From Barcelona to Madrid, there are many buses/day, but it's a long haul...about 8 hours, at a cost of 28 Euro. Click here for those schedules and prices. If you want to splurge, you can book train tickets at the above RENFE site for the fast AVE up to 62 days in advance for as low as 46 Euro...under three hours.
These sources will also work for the reverse journey.
To save yourself some time, you may want to see if you can fly into Madrid and out of Barcelona (or vice versa) on an open-jaws or "multi-city" ticket...to save yourself a day returning to your starting point.
But if you have no compelling reasons to visit Cuenca or Valencia, I would suggest a route along the lines of Madrid-Sevilla-Granada-Barcelona...much more interesting, IMHO.

Thanks for the input. We're actually a touring classical choral group, and the bus is chartered. We have engagements in those cities, hence the "must go" directive. I was concerned about getting from Valencia to Barcelona; I've heard the coastline is not very scenic. Is this true? Would it be a more interesting trip if we went Madrid-Valencia-Cuenca-Barcelona? Is the interior of Spain more interesting?

Not really. You'll be backtracking some with the alternate route, and the plains of the interior plateau can get boring, unless you're a prairie kid, like me. :) Stick with the coastal run.