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@mattty
Yep. The way cycle to work operates is that your employer pays for the bike up front, then leases it to you for 12 months. Thus they bear the risk of you defaulting. This risk is quite low, though, as (a) they employee you, and (b) they take the payment from your pay packet every month.
The discounts simply come from tax relief: your installments are taken from your gross pay, so you don't pay any income tax or national insurance on it. This is just a way for the government to subsidise the bicycle (as they are forgoing that tax revenue).
So in theory, you could persuade the government to subsidise students as well, but the absence of (a) the risk-free (for the gov) repayment mechanism, and (b) a simple way to administer the subsidy, the cost of implementing the scheme could outweigh the benefits.