Oops! Sorry, I thought I'd done that one yesterday. I typed an answer but, well, I'm working now so CC access is limited so I might have had a panic Alt-F4.

(I started typing this reply at about 3pm, wonder when it'll get posted)
Your employer would need to accept an invoice from you as a legitimate business supplier, subject to all the due dilligence requirements that your company has. You would need to set yourself up as a business, probably as a sole trader, and most companies would require you to issue an invoice for their asset records.
It might be easier, though, for you to buy the bits on the scheme and not charge for building. I don't think that the regs say that you need to buy a complete bike, but it does say "Eligible equipment includes cycles and cyclists' safety equipment".