Motorcycle and Scooter appreciation

Who knows the law regarding riding an untaxed and unmoted bike to the test centre?

I have bought a bike on eBay and it's not got either of these things. I think if I book it in for an mot I can ride it to the centre. As far as I know it's meant to be ridden to your local/the closest test centre but I would book it in to the centre closest to my home, which is about 15/20 miles from where the bike is currently located so I'll probably ride past several test centres on my way to the one where I'll book it into. Im pretty sure I can blag that if I get stopped.

Seller says it'll go straight through an mot you never know so if it fails I'll need to ride it home, that'll be totally illegal I think but by booking into the test centre that I will, it's almost just round the corner so should be alright. Unless the test centre done the po-po.

Sound like a sensible plan or have I got the laws completely wrong?

You must be insured.
Other than that you don't need MoT or tax, but the appointment must be pre-booked.
There is no legal requirement to go to the nearest test centre. You can go to whichever is most convenient to you.
If it fails it is still perfectly legal to ride it home, and it is legal to ride it to places for the purpose of having MoT failure points fixed.
I'm guessing there is a time limit (perhaps the free re-test limit) but I don't know.