Switzerland in mid-November?

Too early to ski, too late to hike (usually). Perhaps you can find a good hike at lower altitude, but the high pastures will likely be covered in snow.

This is probably the worst month of the year to experience the Alps. I'd suggest to concentrate on what "urban" Switzerland has to offer with museums and sights. Bern is not far from Bulle and certainly worth a daytrip.

Bulle is in the French speaking part of Switzerland with a very different culture from what you'd see in the other areas. Could be interesting to explore that part!

Bulle is just a stones throw from Gruyere. People pay good money to ride the "chocolate" train to tour the chocolate and cheese factories located there. There is the Golden Pass railway there going to Montreux to the south or Zweisimmen to the west. You'll be able to size up the snow (or lack thereof) when you get there.
There is plenty of good hiking in the lower mountains. Snow is unusual along Lake Leman (Geneva). Last year I landed at Zurich in January and I commented that it was the first time in a half dozen or January touchdowns that I ever saw snow on the ground there. The same day, Geneva was sunny and (relatively) warm.

Thanks for the advice.

Thanks again for the advice. Taking the season and my interests into account, I thought about what I would enjoy even if the weather was gloomy, so I've stitched together a tour of castles in the western part of the country. I'll spend more time in the French speaking areas, but will venture into some of the German speaking areas as well. I leave in just under month.