The halfway point of our five-day, three-country trip on two wheels around Lake Constance — known as the Bodensee in German — had been long, hot and a little bloody, as I’d taken a tumble off my bike.

Then, just minutes from our hotel in Uberlingen, Germany, my sister Lee and I were separated by a marching band on its way to the city center. Intent on finding her, I ignored the festivities. But after we were reunited and revived with showers and dinner, we set out to indulge in a truly German tradition: a soak at the local spa.

The monthly late-night special at Bodensee Therme appeals to locals as well as bargain-hunting tourists. Thirty-five euros buys four hours of soaking starting at 10 p.m. and access to an all-you-can-eat buffet.

There’s one catch: The spa becomes a Nacktzone — as in, nudity is mandatory.

Our limbs were aching, and the only way into the steaming pool of promised relief was to throw aside modesty along with our clothing. So we did. Moments later four elderly, overweight German men joined us.

Bathing with naked strangers was one of several challenges presented and overcome on our cycling adventure around Lake Constance, one of the more popular bike trips in Europe. An estimated 400,000 people ride all or part of the 168-mile Bodensee trail each year. The path, nestled on a plateau 1,300 feet above sea level, takes cyclists through Germany (107 miles), Switzerland (44 miles) and Austria (17 miles). All of the larger cities have bike rental facilities and pedaler-­friendly hotels. Riders can carry their supplies in panniers or arrange for bike shops or tour operators to deliver their bags to overnight stops, which is what we did, using the services of Radweg-Reisen (cycling-­holiday.com).

Lee and I started in Bregenz, Austria, 90 minutes by train from Zurich International Airport. We allowed ourselves a day to adjust to the time zone and spent the morning exploring the city’s mile-long lakefront promenade and its floating opera stage, featured in the 2008 James Bond movie “Quantum of Solace.” We rode a cable car 1,700 feet to the top of Pfander Mountain and took in the view of the great lake below. It was a little intimidating. Could we really ride all the way around it?

The next day, we started our 40-mile leg through the shard of Austria and a slightly larger swath of Switzerland. That day’s destination, the lively and quirky German city of Constance, welcomed our arrival with a 30-foot statue of a mostly unclothed prostitute presiding over the harbor.

No, we hadn’t entered another Nacktzone. We’d come upon the Peter Lenk statue of the courtesan Imperia, a symbol of midmillennial debauchery, religious fervor and political chicanery that accompanied the Council of Constance, 1414 to 1418.

“Everything you can have — crime, sex, politics, history, everything,” happened during those four years when the papacy was whittled from three men to one, guide Henry Gerlach told me during a walking tour.

After hearing about the seamy side of 15th-century life, we headed to the nearby garden island of Mainau, third-largest island on the lake with lots of floral eye candy, from giant Disney-­like topiaries to fields of roses.

Thoughts of torture and bloodshed remained at bay until Day 3, when Lee and I left the trail for a 12-mile side trip to Salem and its monastery, palace and shops. During the uphill journey on loose gravel, Lee took a spill and I soon followed, priming us for the hot tub — if not for our bathing companions — when we finally rolled into Uberlingen that night.

Thankfully, Day 4 was easy. The historic city of Meersburg, just 7 miles away, is another charming German village with an even more adorable upper village. The nearby vineyards in Hagnau were our next stop.

This region of the lake has been producing wine for 136 years. A consortium of family-­owned vineyards offers cellar tours and tastings.

We stopped at the Zeppelin Museum in Friedrichs- hafen and then made our way through rich farmland to the island of Lindau, stopping at roadside stands to stuff ourselves with local cherries. We walked our bikes through Lindau’s main plaza to the old Church of St. Peter, where the Passion frescoes are from the early 1500s.

The sun was low by the time we finished the circuit back in Bregenz. We snapped selfies and took pride in knowing that we’d ventured out of our comfort zone — even into the Nacktzone — and it turned out just fine.