Now in Orvieto and would like to go to falls tomorrow via public transport. How?
I don't have an answer for you; I hope someone else does. This is the sort of question that sends me straight to the local tourist office, but I realize that at this point the Orvieto T.O. is probably closed.
Edited to add: Rome2Rio.com is of some help here, but you should verify the specifics locally. It says there's a 2-hour bus trip to Pentima followed by a short bus trip to Galleto, then a walk of about 0.8 miles. Rome2Rio is not necessaruly accurate about travel times or frequencies, but I'm concerned that it says that first bus leg only runs once a day. You can look for the actual schedule on the fsbusitalia.it website. The bus number is apparently E653.
The short trip to Galleto is Bus E621, operated by the same company.
This sort of thing is tricky. Be sure you'll be able to get transportation back to Orvieto.