Please stop worrying about this, neither you nor your sister could have infected your neighbor from the distances and limited exposures you are talking about.

The fact that he was very old and so frail that he was bedridden undoubtedly meant he was in very failing health already. The most common reason for death in this case usually whatever disease(s) he might have had, pneumonia from lying in bed (fluid accumulates in the lungs and the body is too weak to fight) or failure of his heart.