I don't see why you should have to prepare for the dog coming into your garden again. You have worked hard to get your home and you obviously enjoy your garden, to date.
There is an attack waiting to happen, imho. I might get an air horn to summon help - presumably Mr Bm is not always out in the garden with you - but that will not protect you from the dog. You cannot rely upon the owners always putting a muzzle on the dog before letting it out of the house. Having a stick or even a garden fork ready will not necessarily help you. Secondary fencing, at your expense, might be a way of re-enforcing the breached boundary. I wonder if the dog used the same entrance to your garden on the 2 occasions?
I have had a doberman - soft as putty, and GSD's - good guard dogs but always under control. I would say to hell with relations and report the dog to the police and I am a great dog lover!