Not if he knew there were loose ends in the house that needed tidying up, the silencer and hidden phone for example.
Bamber could never be sure he was safe, someone could come forward days or weeks latter saying they saw a cyclist on the sea wall in the middle of the night or something like that on hearing of the tragedy.
No killer can ever be sure of being safe, does that stop them….no it doesn’t. The moment they leave the house they take the risk of being seen. Saying they saw a cyclist on the sea wall a month after doesn’t automatically mean it’s Bamber, he has to be recognised and identified as well, yes it might go against him but it doesn’t automatically convict him.
If everyone could commit murder and know they were safe I’m sure there would be a lot more murders committed.
He wouldn’t be bothered once the Police had finished their investigation as far as he was concerned it was accepted as murder suicide.