Not sure I can be of any help. I have been in Umbria many times (based in beautiful Spoleto) but don't drive. I have travelled by train to Assisi from Spoleto and visa versa. I have also travelled by bus from Spoleto to Cascia and back again to Spoleto.
Cascia , as far as I know, is not on any railway line. I don't know if there is any (public transport) direct link from Assisi to Cascia. You may be forced either to drive or hire a driver. On hiring a driver one of the recent posts on the Spoleto forum talks of a Umbrian driving firm you can contact - I've never used them so I can't comment or recommend.
(As a slight aside Rome may be another common denominator. From Rome you can get a train to Assisi. From Rome you can also catch a bus to Cascia. If you are interested in these options I can find the relevant links for you. One word of caution on the train to Assisi, the train arrives at the edge of Assisi, and then you have to take a bus to Assisi proper).
My best wishes.
Then bus from the train station, which is Spoleto Stazione on the timetable umbriamobilita.it/public/…E401.pdf There are few direct buses to Cascia, but there are additional connecting buses from Norcia - click Cascia on umbriamobilita.it/it/… to find the PDFs to download.
I traveled to Umbria in November of 2012. Not wanting to rent a car or waste time sitting on buses & trains when there is so much to see & do; I researched hiring a driver & guide. There were several recommendations for Gianluca Siena of Umbria Driver in TripAdvisor forums, so I contacted Gianluca by email & he helped arrange the trip. Gianluca is born and raised in Umbria, so his advice was priceless. My friends & I saw all the high points like Assisi, Spello and Trevi; but also a chestnut festival in a village so small it’s not on any map! Watching, learning and actually picking olives at a harvest and tasting the new olive oil at the local cooperative olive mill.
This is the way to see Umbria! Gianluca’s service was professional, reliable and very reasonably priced. When our itinerary with him was complete, it was like saying goodbye to a good friend. I highly recommend Umbria Driver for the best possible way to see Umbria. See Gianluca’s website at http://www.umbriadriver.com/sito/about-us/
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