Jeremy could have entered via the bathroom window, though I doubt that he ever used a hacksaw blade to do so, as it's an unsuitable instrument. He could possibly have exited via either the bathroom window or the kitchen window, but he claimed he didn't know how to close either behind him. On a separate occasion, he gained admittance without a key, but left a note for the housekeeper (or for BW, asking her to ask the housekeeper), asking her to fasten the window he'd used.