David has gone to a lot of trouble to incriminate Julie, all to no avail. It's quite possible that Jeremy was told about the bible being on Sheila's chest by Police that first morning, and as we know anyway the scene was not exactly as recorded in the photographs by PC Bird as was related by another Police Officer(whose name escapes me for the moment). Why on earth would Julie introduce Matthew Macdonald into the equation if she's desperate to be believed at this stage? The sum of £2000 was the debt Jeremy owed his father and therefore probably stuck in his head, and as in the David Bain case debts can play a part in the demise of another.
The point about the second telephone call as DS Jones asked is why telephone Julie at all, if not to impart to her that all the family had been killed? The telephone call is crucial, not the timing of it but the fact that it gives Jeremy knowledge of the crime at that early stage.
As for the bicycle, it was at Bourtree Cottage when Julie arrived on Saturday 3rd August and remained for a month after the murders. It was covered in the yellow sulphurous mud typical of the area suggesting that it had been used at one point, and unlikely to be a female being left in that state.