public transportation to white villages(NOT Ronda)from Cordoba or Malaga and to Cadiz

I looked at your post thinking you wanted guidance on 'Andalucia using ONLY trains and buses' which is certainly feasible and I can help with - is there a query here, as the full text mentions nothing of this?

The white villages or towns are many and I am not sure what you expect from them but with five days in one of the villages or even a larger town, I suggest many would struggle to maintain an interest, unless you are happy with (could be very) sleepy.

Hi Neil...I guess my reference is to availability of public transportation to the white villages from Cordoba and to Cadiz..sorry for the confusion..and we do like sleepy and slow paced...also, if there are lodging recommendations in Cordoba(in or close to the Jewish quarter)and Cadiz, I would appreciate it..thanks

Melinda, since you are both over 65, and you may be traveling a bit by train in Spain, you might be interested in the Tarjeta Dorada (Gold Card). You buy it in any staffed train station for about 5.20Euro. It provides a 40% discount on tickets for travel on Mon-Thur. The discount if 25% for travel on Fri-Sun. Just buy it before you buy tickets for any other Spanish train travel. We've done that and it works quite well.

You can always catch a bus to anywhere. They're cheap, generally not sold out, nice charter buses. There are multiple companies competing (unlike Greyhound). Every bus station I've been in has a customer information desk with an English speaker who can explain your options and help you purchase your ticket. Alternatively, you can visit a travel agent in town who will do the same as the information desk (American travel agents won't know anything about Spanish buses because they don't get commission).

I like to buy my ticket the night before, or when I arrive in town, just so I know when and where to be and can plan around it.

Some cities are well served by train, but that's the exception rather than rule in Spain. Trains cost a lot more unless you book well in advance.

I think if you try a bus trip, or two, you will quickly get comfortable with them.

It was about 10 years ago, but we found the Hotel Mezquita in Cordoba to be very good. Clean, charming, good breakfast, nice service, and easy on the budget. As the name suggests, it's very close to the Mezquita. I'm remembering across the street.

There are scores of towns and villages which are referred to as pueblos blancos in the Cadiz, Seville and Malaga provinces and are attractive from a distance and might have something of interest for a few hours or an overnight. I strongly suggest you do more research.
There is certainly no one route to link any more than a very few by public transport and buses are not scheduled around the tourist's needs. It is true, as Brad says, a bus touches almost everywhere, but that could be just twice a day and not at all at a weekend. And yes you would be able to link Cordoba with Cadiz via wherever with several buses or trains.

Without a specific destination all I can do is give you some information for bus companies or transport hubs which may be useful and may or may not be in any good guide.

http://www.tgcomes.es/index.asp

http://www.activagest.com/linesur/horarios.htm

http://www.estacionautobusescordoba.es/

http://www.turismoderonda.es/informacion/pdf/horarioautobuses.pdf

And train - www.renfe.com

Malaga to Cordoba by train or www.alsa.es bus if not already aware.

I would clarify - it would be highly unusual to find bus company competition on any specific route.

I will help more if you cannot find your way once you have a more solid itinerary.