This series of novels is not meant for small children, but older children certainly can read them and enjoy them, and while bicycles are not the theme, at least one bicycle is prominent in many of the stories.
These are Alan Bradley’s crime mysteries series featuring 11-year-old enfant precoce Flavia de Luce, youngest of an ancient, decayed, and near bankrupt rural aristocratic family, who has a genius for using chemistry to solve crimes, to the discomfiture of the regional police. She appropriates her long-ago-disappeared mother’s BSA Keep Fit that she names Gladys to ride about her family's little ancestral village of Bishop’s Lacey investing things.
The 3-4-5 earliest ones are the best ones.
Bradley does due diligence in his historical research and writes in a detached and whimsical/ironic but engaging way.

No book to link this photo to, but the photo shows 2 boys in Belfast long ago, one a very famous writer. A pat on the back if you can identify them.