OP,
So, somebody got into your house and took your keys, despite the fact you had closed the door behind you. The intruder cannot have entered via the back, because at least one of your dogs would have noticed, and you might have seen them too.
I am wondering who has legitimately entered your house, perhaps to carry out work - or even for a few minutes, and whether they might have deliberately stolen your keys in order to harass you, for whatever reason, possibly because they are just odd. Where do you usually keep the keys, and had you tended to leave them where they were easy to see?
I think you should provide the police with all the details you describe. They might want to know who has entered your property, even legitimately. I cannot otherwise explain how they entered a closed door to steal your keys. Also, who, in your family, has a key? Have they lost it and not told you, and was your address written on the key fob?
It seems the key thief may have left the keys on the bus, possibly even deliberately - perhaps to scare you for some reason. So they may have travelled to within walking distance of your property to ensure no recognisable vehicle was nearby. But why did they not simply park their car a few streets away? Maybe they don't drive, have a car, or maybe parking is difficult?
Take care OP!
Wildlife cameras are a good idea, and can film in the dark.