Reckless is not an adjective that comes to mind when you talk about the Swiss, particularly in Bern, their rather staid capital. Yet here I am, submerged in the Aare River, being swept away by its powerful current. If I don’t get out by the Swiss Parliament, there’s a risk of going over the weir and certain injury.

But the Bernese women cruising past me, hair immaculate, don’t seem to be too worried. They’re carrying on like this is something they do every day.

In fact, they probably do. In the summer, the way Bern residents keep cool is to plunge into the river, often with their clothes and shoes in a special waterproof bag, and float down to the Marzili, a complex of pools right on the riverside. Even politicians have been known to join them in their lunch breaks.

I’ve left my clothes in a locker here and walked up river for around a kilometre before holding my breath and jumping in.

The temperature is around 20°C so it’s not too cold, but after 15 minutes I’m ready to get out. As well as steps and handrails there’s a special channel leading from the river to the safety of the outdoor pool. This sounds more difficult than it actually is, although you do need to be a confident swimmer.

There are also strict safety rules — no alcohol or drugs, leave your airbeds behind and don’t dive into cloudy water. At times, when there’s heavy rain in the mountains, the river becomes a murky torrent, concealing floating pieces of wood.

Mercifully today the water is crystal clear and the sun is shining. It’s a fantastic experience, one I can heartily recommend.

The river itself bends tightly around Bern’s old town. Founded in the 12th century on high ground, it’s Unesco-protected and the layout of its wide streets goes back to its mediaeval origins when the Aare made it easy to defend.

The story goes that Berthold V, Duke of Zähringen declared that he would name his new settlement after the first animal he found hunting in the forest. It was a bear — in German, “bears” translates as Bären — and this became both the name and the symbol of the city.

In 1513, the Bernese returned home victorious from the Battle of Novara in northern Italy, carrying a living bear as spoils of war. More followed and they were housed in a bear pit in the town’s square, appropriately called Bärenplatz.

There are still three brown bears living in the city, although since 2009 they’re been housed in more humane conditions, in a spacious tiered enclosure by the river.

For a capital, the city is tiny and it’s easy to wander around on foot. The Zytglogge, or clock tower, was built early in the 13th century as Bern’s western gate and subsequently enlarged.

It houses the bells and an astronomical clock with a mechanism manufactured on-site, between 1527 and 1530, by Kaspar Brunner. It’s still going strong; you can climb up inside and watch the complex whirring of cogs and gears as it reaches the hour. A large bellows makes a rooster crow, then there’s a roundabout of twirling bears, before bearded Chronos, the Greek god of time, strikes the bell.

Time was also important for Albert Einstein, who lived just down the street for two years from 1903, when he worked at the Patent Office. This is when he came up with his special theory of relativity and his apartment has been restored and furnished in period style. It’s open to visitors and documents the life of the physicist during his years in Bern.

Another famous resident was Paul Klee, one of the 20th century’s most important artists. His family came here in 1880 when he was just one year old and, as a young man, filled countless sketchbooks with views of the city.

He moved to Germany in 1906, but his art was labelled as “degenerate” by the Nazis and in 1933 he was forced to return, dying in 1940 after his most productive year, creating 1,253 recorded works in 1939.

In 1997, his daughter-in-law, Livia Klee-Meyer, donated her inheritance of almost 690 pieces to the city and the Zentrum Paul Klee was built to house them. It’s a stunning wave-shaped steel and glass structure containing more than 4,000 of his works, designed by architect Renzo Piano.

The building’s three curved “hills” and gently contoured lines blend into the surrounding rolling landscape and a network of 18 paths are named after Klee’s masterpieces.

The city’s own hill — Gurten, known as Bern’s mountain — rises to only 858m but it’s worth taking the funicular up. A network of running, cycling and walking trails caters for Bern fitness fanatics, and on a clear day, the city is laid out in front of you, with the sparkling Aare River running through the centre and views across to the snowy peaks of the Bernese Oberland.

If you are interested in the history of the mountains, the Swiss Alpine Museum tackles current mountain issues from all over the world in an unconventional way, with a series of temporary exhibitions. I liked the Memories Lost and Found, which has a collection of skiing gear over the ages.

The Alpine Workshop also highlights mountain crafts including violin making and weaving, and you can even practise your own skills.

For those craving the real outdoors, just outside the city is the town of Schwarzenburg, the gateway to the Gantrisch Nature Park and the mountains of the same name, rising to over 2,000m.

If you’re not feeling confident enough to tackle those, then anyone can access the Gäggersteg, a wooden jetty in the middle of the forest reserve. When it’s clear, night hikes offer magnificent star gazing.

Of course, Switzerland is famous for its cheeses and a little further away is Affoltern, in the Emme valley, home to the famous Emmental cheese dairy.

This has both a modern production facility and a reconstructed 18th century farmhouse where you can see the cheese made over an open fire. The name “Emmentaler AOP” is protected and only fresh unpasteurised milk from local grass-fed cows can be used.

The cheese has to be matured for at least four months and this is when the famous holes develop — a result of trapped carbon dioxide produced by fermentation.

It’s fascinating to visit the cellars and see the 100kg wheels, each worth around £2,000, stacked in rows. The longer they age, the more expensive they become, and I sample the oldest, at 24 months.

It’s strong but there’s still a hint of meadow flowers, a delicious souvenir of my visit to Bern.

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