Do they?
Bamber took June's bike back to his cottage before the massacre.
The official police theory, as set out in Mike Ainsley's submission to the DPP in 1985, is that Jeremy went on foot and used the bicycle on the return leg.
It may be that he also had the bike at the cottage earlier than the incident, but wouldn't that lend weight to his own story and his innocence? You seem to be backing up Jeremy on this point. Thanks Adam.