A number of issues.
Bicycles have VAT charged on them.
Local roads are maintained from local funds (Council Tax, the govt. grant to the authority, business rates etc.) which are paid by everyone.
Trunk roads are paid for centrally, from taxes paid by everyone.
A 1 Tonne (1000kg) car damages roads faster than a 100kg bike (incl. rider). It's a 4th power law so the rate is 10x10x10x10 = 10000 times as fast. If VED was based on that, and an average car VED was £150 then a bike should pay 1.5p a year!
The massive cost of signalling roads is only necessary because of car use.
Cars cause ill health and death. Bikes don't. Tobacco duty is justified on these grounds, no reason why motor vehicle duty shouldn't be as well. (I wouldn't push that one as it doesn't stand too much scrutiny for tobacco!)
IM (not at all H) O motor vehicles should be taxed enough to pay the costs of maintaining and building roads, to fund the total health costs of our using them, to compensate for the damage from pollution including that to buildings and agriculture, and anything and everything else that could possibly be attributed to them, then perhaps they'd go away!