Ballpark estimate of travel cost between Bern and Gimmelwald

www.sbb.ch/en Input from: Bern to: Gimmelwald and any date within the next 30 days, convenient time. Then click the red box "search for connection". You'll see all the times, click on the red price box on the right. The price you see will be the "Half fare" price. Double that if you don't have a Half Fare Card.

I suspect you'll want to know more than just that trip. For example, once in Gimmelwald, are you just going to sit there, or perhaps take the cable car up to the Schilthorn, or down to Stechelberg, or trains up to Wengen, or Kleine Scheidegg? In any case, you might also want to consider the Berner Oberland Pass (Google it), which is good from Bern on south, includes most cable cars and mountain trains, and is generally cheaper.
Here's some places to look up prices:

https://www.jungfrau.ch/en-gb/prices-and-brochures/

https://www.sbb.ch/en

From this last website, I entered Bern to Gimmelwald on a random day, and it said half fare card holders pay 23 CHF (about $23) one way, so a regular fare one way is 46 CHF.

As of 2018 the Swiss Travel Pass now includes travel to the top of the Schilthorn for the first time, this used to be around 45 CHF addon with the old Swiss Pass (or the half fare card), but now you can make multiple journeys to Birg and Schilthorn with the pass inclusive.

For the journey you mention the 2nd class single is currently 23CHF without additional discounts.

Cheers,
Tim at the Mittaghorn

When I look at the SBB site, seems that 23 CHF is the price if you have a Half Fare Card. Without one it would be 46 CHF