One of our connections in Andalucia in May is from Arcos de la Frontera to Olvera by bus (with bikes underneath). If we take a mid-morning bus, we can make a 4 hour layover partway (just to see another village). The options for layover are Bornos, Villamartin, Algodonales or Puerto Serrano (may be there briefly another day - cycling the Via Verde from Olvera), We would have time to cycle just a bit outside the village as well, if that would be worthwhile. They all have a mid-afternoon bus to Olvera. If you had just 4 hours in one of these villages, which would you choose and why?
Are you road biking or mountain biking? Are you looking for flat road or like a challenge of climbing for a rewarding descent? I have never been to any of the towns you mentioned but when I googled "biking in (one of the towns you mentioned), a lot comes up for bike routes. I wonder if you would get better responses on a bike forum. We are mountain bikers and use MTBR.com forum; we asked a bunch of questions about what we were to expect, biking in the Sierra Nevada mountains, some of the highest ranges in Europe (or so I was told). We are from Florida and know nothing of altitude, mountains, or cold weather cycling. You being from Colorado, should have minimal issues biking in elevation. I asked a few biking questions on this forum and got minimal assistance. the only downside to mountain cycling (or perhaps any kind of cycling) in such beautiful areas is that the beautiful scenery goes by you so quickly and unfortunately my eye is right in front of me, following the appropriate bike line. So having said this, remember to stop every once and awhile and look around at what is around you. It can bring a tear to the eye, it is so beautiful. Biking in Andalusia was the best experience of my life.