Many people vacationing in Umbria usually tend to consider Siena as a destination to plan a day trip.
However, Siena is not so well connected to Umbria by public transport, so a day trip from the towns of Umbria — Perugia, Assisi, Gubbio, Todi etc… — would not be a so good idea.
As an example, traveling from Perugia to Siena — the shortest and best connected route you could consider when planning a trip to Siena from Umbria — it will take you 3 to 4 hours if you make the trip by train, also requiring you to change a couple of trains.
Better if you go by bus. A bus trip from Perugia to Siena will take you one and half hours.
However the timetable does not fit your trip needs. Bus leaves Perugia 5.30PM. For return trip, it leaves Siena at 11.40 AM.
That means you’ll have to spend a night in Siena — or in Umbria if you are planning a day trip in the opposite direction.
Bottom line: a day trip to Siena from Umbria is not a possibility.