Bicycles On Stamps...

Not a helmet in sight
Became compulsory in 2003
RIP Andrei Kivilev.
Winner 1998 "The Pirate" Marco Pantani.

On March 12, 2001 Singapore issued a set of four stamps to commemorate Commonwealth Day. The $1 stamp (S.G.#1091) from the set depicts cycling and other sports.

Hungary
History of Bicycles
February 20, 2002
The stamp set depicts large wheel bicycle, tricycle, bicycle, and tandem bicycle.

Bicycles are featured on several of the stamps from Singapore's "50 Years of Tourism" set of five from 2014. Two cyclists are shown on the 2nd local Rate value, and a bicycle with a side car is depicted on the 90c stamp.

On September 9, 2010 Germany issued this stamp (Mi. #2820) commemorating the bicentenary of Oktoberfest. On the right side of the stamp, woman can be seen on a penny-farthing.

From Wikipedia, "The penny-farthing, also known as a high wheel, high wheeler and ordinary, was the first machine to be called a 'bicycle'. It was popular in the 1870s and 1880s, with the large front wheel providing high speeds (owing to it traveling a large distance for every rotation of the legs) and comfort (the large wheel provides greater shock absorption)."

Singapore 2020 Police on bicycle patrol.

Singapore 2019 Cycling at the East Coast Park.

Singapore 2019 Two little figures of cyclists near the centre of the single stamp in the miniature sheet.

Belgium used a child's drawing as the design for their 2000 Christmas/New Year's stamp. A postman and his bicycle are depicted.

Israel
Cycling in Israel
July 16, 2019
The stamp set depicts mountain cycling, road cycling, and urban cycling.

On January 5, 1993 The Netherlands issued a set of two stamps to commemorate the 100th anniversary of bicycle and automotive manufacturing in the country. The 70c value (Sc #821) shows recreational bicycle riding.

Here is Canada's March 3, 1997 issue (Sc #1636) commemorating the 75th anniversary of the founding of Canadian Tire by J. W. and A. J. Billes.

Canada issued this 48c stamp (Sc #1998) on September 10, 2003 to commemorate the Road World Championships at Hamilton, Ontario. Format is single-pane booklet of eight.

On June 23, 1989 Canada issued a set of four, 38c "early Canadian photographers" stamps. These stamps were printed se-tenant fashion in traditional sheet format. One of the stamps honors Jules-Ernest Livernois (1851-1933), a second generation photographer from Quebec. The stamp (Sc #12140) shows a Livernois photograph of a man riding a penny-farthing.

Not sure if this qualifies in a bicycle thread since this
was the De Dion Bouton motor tricycle.
But it looks more like a bicycle than an automobile IMO
even though it was issued for the 75th Anniversary of
the Austrian Automobile Association.

AUSTRIA

Scott 989