I was in Badajoz for about ten to twelve days some years ago and at the time there was one or two coach services per day to Lisbon one of which used leave Badajoz around midnight if my memory serves me correctly.
I can concur that Badajoz is indeed a lovely little Spanish city - there was a lot of development going on when I was there and I seem to recall a very old building was being done up to be the new law faculty of the university. I remember the plans impressing me anyway.
Good luck to Helitt - I hope they will not turn out to be a route prover for Ryanair. I think Barcelona or Girona to Badajoz would work pretty well in a Ryanair type operation. The motorway road journey to Madrid does indeed take about 4 hours and in my case at least the train was a lot longer! Maybe it was the slow train!