You don't have to use any of the official schemes at all. It's absolutely fine to buy the bike online (obviously in the firm's name), and then put the expense through the books.
As mentioned above, if the firm isn't VAT registered then you can't claim the VAT back.
Normally though if you, or any other employee then uses the firm's assets ie the bike, then it would be a P11D taxable benefit. The Cycle to Work scheme merely confirms that provided at least 50% of the bike's journeys are for commuting to work, then it's not a taxable perk.
Generally employees are expected to repay the cost of the bike purchase, but as this is done by reducing their salary, payment is net of tax and employees NI, so means savings of up to 32% compared with the employee buying the bike themselves out of taxed income.
However, there's no requirement for the employer to make the employee repay the net amount, so if you run your own company, I wouldn't bother!
Full HMRC guidance is shown here.
Good post.
Just to clarify, dependent on the employee's tax bracket savings can reach 52% if a higher rate taxpayer, but this is before you come to the transfer of ownership debacle.
I don't believe there is a requirement for the hire payments to offset the original purchase price, so you might as well use the bike without paying anything until it can be written off as having a nominal value after 6 years. I'd like to check this though,