Ok, I currently pay £51.06 before tax for my £720 cycle to work bike. This equates to £35.23 after tax, according to the online calculator. I am considering getting a £1000 bike, which would be £70.92/£48.94 according to the same calculator.
However it assumes a 647L tax code, but mine is 403L. What difference does this make to a) the savings I will get overall and b) how much money goes out of my wage after tax (the calculator says I'll essentially pay £13.71 more, but does my different tax code make this less or more???)

I can't figure it out!!!

The different tax code allowances won't make any difference to the figures as the savings come out of the taxable portion of your salary.
Unless of course the deductions took your salary below the tax allowance – but I am assuming that is not the case.

As Coleman said.