Zurich to Umbria

Buses serve this route, Flixbus for one, there are probably others. Between 6 to 8
hours to go from Zurich to Perugia.

There are trains from Zurich to Milan every hour until 1:33 pm with a couple later trains, takin 3 hours and 20 minutes. Faster than any bus.
www.sbb.ch/en

SBB the Swiss transportation company, shows the possibility of a less than 9 hour journey: Zürich to Milan to Firenze to Perugia. Look at www.sbb.ch/en for other options but that is the easiest route with the least number of changes,

Hi there,
You can search the Swiss rail carrier, SBB, for this route (https://www.sbb.ch/en). It's a long journey. As an example, I put in Tuesday as a departure date, leaving before 8am. The route is Lugano-Milan-Florence (or Bologna) - Perugia. The whole trip would take about 9 hours. You can buy your tickets on the SBB site. I would also check to see if there's a difference in price buying Zurich-Lugano or Milan on SBB and the rest of the route on Trenitalia. If you buy on SBB, take care with the box that asks whether you have a half-fare (discount) card or not.
Cheers!

We used trains from Zurich to Chur to Tirano, part on Bernina express. From Tirano, there is a direct train to Milan. If you don't want to take the Bernina Express route, there are routes Zurich to Milan. I advise looking at Google maps for a start. There are multiple ways to accomplish the route. Some go thru Rome, some thru Florence, and there were others. It really depends on what you want out of the journey. We chose to fly into Zurich on one of our trips to Italy because it was a much cheaper ticket and because we thought it'd be fun to use to Bernina Express.

When is this going to be?

Zürich to Perugia takes a bit under 8 hours by train. Best place to book is Trenitalia. However you must spell the city as Zuerich