Creeping has never been my thing
Bicycles have moving mechanical parts that make noises. In the main legs and feet don't. Of course footwear has the potential to leave footprints and evidence adhering to them by way of blood and soil but this would also apply to bicyle tyres.
Not even when you're wearing sneakers?
Maybe June's bike was well-oiled?
In a dry August what are the chances of mud adhering to the tyres, especially on the B1026 Maldon and B1023 Tollesbury Roads?
I was surprised at the total lack of any street lighting from Head Street/Church Street all the way to Pages Lane on a Streetview walkthrough, which makes me even more convinced that JB chose to pedal either the GREEN or RED route, but more likely the shorter latter one. Quite a few new houses appear have been built along Church Street, which means with fewer residents in '85 there was less chance of him being seen pedalling home like the clappers to break the news of his successful venture to Julie. I think you'll agree.
Just noticed in the Julie's interview you posted that she said JB would use the "back road" which to me means the RED route that passes the neighbouring Hyde Farm before coming out onto Maldon Road.
If Jeremy had his own bike, I'm certain that would have been forensically examined and we'd have heard about it.