Well maybe not, but it's more plausible than him hitching a ride with a flying saucer. 
I think why some of the guilty persuasion keep on mentioning a bike is that it makes everything that Jeremy did suspicious. So the more suspicious they make these things he does efore the murders the more guilty that making him look. Things like, "Oh look he ate a hearty breakfast. He must be guilty if he could do that". Or, "Yes isn't it suspicious. He borrowed his mum's bike and made out it was for Julie. Now that is suspicious isn't it? "So it gets people thinking that everything he did before the murders were to do with the murders"
But nugnug is right the times in respect of the murders aren't that important at all. In effect he had all the time in the world. Mind you, that's a jolly long walk along the sea wall and across the fields.