I must admit that I have not personally done this particular route by public sector transport.
However, Spanish bus operator Alsa shows a twice daily service at 11:15 and 22:45 running between Evora and Badajoz.
I would recommend the 11:15 one as it allows one to arrive at Badajoz at 13:45. The latter town is not one you really want to arrive in at 01:45 in the morning.
Alsa website:
http://www.alsa.es
Check out Cubsur's site here for more potential info:
http://thomasallen.home.sapo.pt/travel/001.htm
See the section at the bottom of the page on travel between Portugal and Spain
