I think your employer can just self administer if there are only 2 of you.
You would order the bike, let’s say it costs £600, from the shop. (All numbers below made up but they illustrate the point).
Your employer pays the bill so you now owe your employer £600.
They get that £600 back as a £50/month pre tax salary sacrifice deduction from your payslip each month over a year.
Your pre tax salary is £50 lower. But you would have paid £10 tax and £5 National Insurance on that £50 and so only received £35 of it. So you’re only missing out on £35*12=£420 over the year.
Your employer also avoids paying National Insurance (and pension contributions?) on the £50 each month so they also make a payroll saving.
Edit: but at the end of the year you don’t actually own the bike. You can normally pay a nominal amount to extend the ‘lease’ for another few years. Or pay more to purchase it outright, HMRC have a table setting out the % of original price to be used to value the bike.