Buses Evora - Merida.

What day of the week are you traveling?
Alsa has a morning bus 3 times per week.

If that bus doesn't suit you, you can make the route changing buses in Badajoz. For info about the route from Evora to Badajoz, take a look at Rodoviária do Alentejo. For info about the route from Badajoz to Mérida, take a look at the web of Leda.

P.S.: From Badajoz to Mérida, you can take a train if you prefer.

Thanks Anillos, it seems there is also an Alsa bus at 11am for 1 or 2 other days of the week according to the Alsa's website, but the other 2 buses dont appear at all, strange. But that website you provided is perfect for Evora - Badajov, and should suit me well. Gracias otra vez!