Not to interrupt the revelry, but it possibly has something to do with the pronunciation of the word cycle, and when the various types of bikes were named. The word cycle /'saɪkl/ predates the others. It may have been that bicycle was originally pronounced /'baɪsaɪkl/, but that the second of the two diphthongs was reduced by some process of dissimulation /'baɪsɪkl/.

Ceci n'est pas un seing.