People who don't use public libraries still pay for them. People who never use the National Health Service (either because they have private treatment or simply never fall ill) still pay for it. People without children pay for schools and colleges. People who never use sports centres, swimming pools, or theatres pay to subsidise them. People who never go into public parks still pay towards their upkeep. People who don't drive or cycle still pay for roads. It would seem somewhat harsh to separate out cyclists for special treatment!
Additionally, as someone who makes most of his living from conducting interviews on parts of the National Cycle Network, I can tell you that it's often pedestrians who benefit most from new routes being created or existing paths being upgraded. (Further, much of the funding comes from a registered charity [Sustrans] rather than directly from any form of taxation).