Day trips from Urbino using public transport

I've wanted to go to Gubbio for many years but haven't made it yet. It sounds very atmospheric, and it's way off the American-tourist trail. It looks as if buses make the run in 70 to 95 minutes. There are two bus companies connecting Urbino and Gubbio, though not frequently. Adriabus 22R runs twice a day (only once on Sunday). Autolinee Curcio appears to have one bus a day.

I imagine it's easier to get to Pesaro, and you could connect to a train there.

I'd strongly consider having a car for the area, but once you get to Pesaro by bus, you can zip along the coast by train. Senigallia is outstanding.
Urbania might be an option by bus--do you speak Italian by any chance?

Here is one schedule--Fano is a really cute little seaside town.
https://www.adriabus.eu/en/orari/

Don't suppose you are from San Antonio? In which case a car is not really a practical idea.

If you should decide to take the bus to Gubbio, be aware that there may be a change midway. I had taken my shoes off to relax and the bus pulled off to the side of the road and the driver stood up and shouted "Cambio, cambio!" He knew there was someone on the bus who needed to change to get to their destination. We got off and sure enough, another bus pulled up on the other side of the road and we got on to continue our journey. It would be nice if you could figure this out ahead of time!