Van, trailer or truck...
There used to be "day insurance" available for over 25s, but that has vanished off the market this spring. Doh!
The bike can be ridden, insurance-wise, by someone else who has "any-other-bike-not-registered-to-self" third party cover. Many bikers have that, I do.
Alternatively you can arrange cover for yourself, and get it taxed too if the old MOT hasn't run out yet. Do that a few days before the MOT, then cancel within 14 days of arranging it - some insurers won't charge you even if cover has begun, so long as you don't make a claim, but others will want an admin fee of £25-35 or more so ask first.
Sadly if the MOT has expired you cannot get tax and cannot legally ride it on the road. In that case then you have to transport it to the MOT test centre on a trailer or in a van etc.
It's pretty stupid really. You are allowed to drive without an MOT to a pre-booked MOT test, but not without tax, tax which you can't get without a valid MOT.. ..Catch 22!
You can legally drive yourself, or anyone else who's eligible to vote, to a polling station during polling hours. So, if there were a general election and an MOT centre next door to the polling station, then your luck could be in, but you'd still need insurance...