All the downstairs windows were supposedly checked by Taff Jones (it's said) and were found to be secure, including the shower-room window, which JB could easily fasten again by means of a rotating catch on top of the lower sliding-sash once he'd climbed inside.
The kitchen window through which he is thought to have exited is the opening casement to the right of the top left fanlight, as discussed in the later posts above. You can just make out one lower hinge on the extreme right and also the darker line of the window itself. JB first opened the top fanlight, cleared some items on the sink, then opened the larger casement window and climbed out of that. Banged it to once outside, then reached through the fanlight to secure the central fastener, if there was one. Then he banged the small fanlight to, to fasten its stay. Don't forget that JB was fit and agile – climbing on and off tractors daily, and doing other manual farming tasks.
Even Paul Harrison believes JB exited through the kitchen window (but also claims that because Sheila unfastened the back door for him, she was involved in a conspiracy).
When interviewed Bamber admitted that he'd previously got in WHF by the Shower room window and others in the past. After the murders too because he had no key, to collect travel documents before going on a freebie Continental jaunt.
Why would a burglar get in through the window, murder everyone including two sleeping children, then steal nothing? JB rang the police saying that it was specifically Sheila going crazy with a gun, not just anyone.