I would think a one-time $10 tax at NEW purchase would be sufficient to compensate for any infrastructure wear from a bicycle..................
If it uses the same roads motor vehicles require licensing to use,
a bicycle should be required to be licensed to use the same roads.
Autos are taxed at the pump to support roads - not just damage, but replacing roads as they end their useful life, repairing damage to roads from weather, signage, lights, etc.
Bicyclists contribute nothing to that.
They freeload.