Good news — the bicyclists already pay the taxes! The majority of bicycle facilities are being paid for out of the Levy to Move Seattle which voters passed in 2016. The Levy is funded by property taxes. I’m a bicyclist and I also pay property taxes.
Keep in mind — the biggest beneficiary of improved bicycle facilities are car drivers. Just imagine how much worse the car commute would be if the 1,200 (often more) bicyclists crossing the West Seattle Bridge each day were in a single occupancy car!