The Swiss air force was founded in 1914 with a very few pilots and mostly civilian aircraft, but it only became an effective force capable of defending the country in the 1930s. It was officially mobilized on August 28th 1939 and was able to obtain a number of German Bf 109, Italian Macchi MC.202, and French Morane D-3800 fighters.
Switzerland suffered losses at the hands of combatants from both sides. The first serious combat involving the Swiss Air Force began in June 1940 with six days of aerial battles in disputed airspace that may have been over France or Switzerland depending on who you asked. The Swiss Air Force acquitted itself rather well.
According to some sources Swiss cities and railway lines were repeatedly bombed by Allied aircraft at the start of the war, beginning with minor, accidental attacks by the Royal Air Force on Geneva, Basel, and Zürich in 1940. Possibly the most egregious occurred 1 April 1944 when 50 B-24 Liberators of the U.S. 14th Combat Bomb Wing bombed Schaffhausen An in-depth investigation showed that weather in France, particularly winds that nearly doubled the ground speed of the U.S. bombers, caused the wing to mistake Schaffhausen for its target at Ludwigshafen am Rhein
There were many more incidents such as these and by the time hostilities ceased, more than 6,500 allied and axis aircraft had penetrated Swiss airspace. Perhaps these incidents were inevitable given the country's location and the Swiss Air Force's use of the Messerschmitt Bf109 aircraft.
In September 1944, the last Swiss airman died in combat, shot down by a P-51 Mustang while escorting a damaged B-17 Flying Fortress to the Dübendorf airfield. After that Swiss aircraft were painted with red and white striped "neutrality markings" around the fuselage and wings to avoid confusion with German aircraft.
Jungmann A-50 carried neutrality markings
As did Jungmeister U-90 and Bestmann A-251
I don't believe there are any Bücker aircraft flying today that carry these markings, but that may soon change as the restoration of Albert and Elisabeth Zeller's Bestmann nears completion. Tom Müller's has also decided to restore Jungmeister U-90 in its original "neutral" marking just like in this picture.
Albert Zeller was kind enough to share this article: Neutralitäts-Bemalung.pdf that documents the design in detail. The text is in German, but the images are self-explanatory, and Google.com/translate will help.