Remember also that 'a fair market price' can quite legitimately take into account that (a) you have paid an excessively high hire charge for the 12 month period - equivalent to the full cost of the bike to the employer, so it will have no written down book value to them at the end of the period;
(
you have looked after and maintained the bike for that 12 month period at no cost to the employer;
(c) if you don't buy, it your employer will have to dispose of it and will incur costs in doing so.
So all in all it is 'fair ' to agree a nominal price and give your employer the certainty of a sale before they agree to hire a bike for you.
If you are being expected to pay full market price (as opposed to fair market price) you should pay a lot lower hire charge - but the tax benefit is on the hire charge, so you want that as high as possible and the purchase price as low as possible.