just talked with someone who's from the Grado area and told me that you can find all the bus schedules to do Trieste-Grado and Grado-Cervignano by bus in here:
http://www.saf.ud.it/ricercaorari.aspx?area*
just checked the Trenitalia site and I can buy any station, not sure why you cannot...
for the trains... see there's different kinds, the slow/cheap ones (or regionale) that basically have lots of stops... and the fast/expensive ones (FrecciaRossa)... the latter is the fastest option... and that one only stops at Firenze S.M. Novella... at the trenitalia site frontpage there's a link to cheap tickets (mini)!!! worth checking!!
I'm also doing the Grado-Ferrara-Firenze minitour!!!