Maybe there was a basket and she only used when required so it would not be stolen.
It is about time you stopped banging on about the bike there is no proof it was or was not used. It is a dead issue.
Personally I feel the arguments either way are stronger that it was not used. It was inherently dangerous to attempt such a ride as I have demonstrated and posted about many times. I lived in the area in the 1970's and am more qualified than you as to the wisdom of using such an approach even JB says it was a non starter and he lived there too.
I occasionally go out on my bike in the middle of the night to indulge in a bit of astrophotography. And locally, the best way to get around is on a bike.
Riding around at night on byways and bridleways through the countryside is safe (relatively), easy and enjoyable. Although I just shoot the stars rather than my entire family. But each to their own.
It would be easy to ride after midnight from GH to WHF. And especially so in august, when it is warm and dry.
As for lights, I use a single, cheap LED light on my bike, rather than the really expensive setups some people use. In the 80's Bamber would have had horrible bulbs and rubbish batteries, but it's amazing how little light you need to negotiate footpaths, byways and bridleways.
Honestly, cycling 3 something miles between GH and WHF at night is easy. He would have been under stress, but as long as he took it steady and didn't go bombing it along at maximum speed along the footpaths, then he'd be fine.
It would be easy to use either roads or footpaths/bridleways/byways.
Of all the logistical problems associated with murdering your entire family 3 miles away from where you live, getting there and back is not very high up on the list, in terms of difficulty.
On another note...
Imagine being Julie Mugford, going out with Jeremy Bamber, a very superficial person, who loved to show off to his friends by flashing the cash, telling you he's got you something....and it's out on the driveway. Oh, lovely, he's brought me a car....oh hang on, it's not a car, it's his mothers bike. WTF? And he tells me I can go and do the shopping on it. WTF? Thanks Jeremy, you really know how to make a woman feel loved. I feel so special now you've stolen your mothers bike so that I can use it to do the shopping.