A major Bern advantage is its vast and busy rail station, located virtually in the town center. An amazing 50 trains per day, starting at 4:50am and ending at 10:14pm, make the approximately 90-minute run to the Zürich Airport. Another 28 daily trains serve the Geneva Airport, a little less than two hours away. Interlaken is just over 45 minutes by train, Lucerne about an hour and a quarter and Lausanne just over an hour.
(Bern is great headquarters for rail pass holders to see most of the western half of the country on daytrips. Here's one suggestion: hop a train for the 40-minute ride to the farming village of Langnau in the Emmental. Walk the town, perhaps visit the local craft museum [Heimatmuseum], then have lunch at the Hotel Hirschen, one of the best kitchens in the region.)
There are also direct connections with the international rail network and Bern is the only European capital served by three different high-speed trains; TGV to Paris, ICE to Frankfurt and Berlin, and the EuroCity to Milan. One can also catch an InterCity night train to Florence and Rome.