Do not assume a rail pass would be the best option, especially for Italy where tickets are cheap.
It will probably be worth it to get a Swiss half price card, especially as this gives you half price on the Jungfrau route as well. It may be worth getting a full Swiss Pass, depending on how much train travel you do.
For Italy, just buy advance purchase tickets to and from Florence. If you have the Swiss ½ price card, that gives you ½ price to the border, and full (Italian) price from the border to Florence.
Why are you basing yourself in Bern? Why not somewhere in the Jungfrau area?