I think Alfred and Diana would get along great. They probably meet accidentally a few times via Bruce, and after that she just sometimes drops by for tea. They like snarking together (about Bruce or the world in general), she enjoys being around someone older who's seen a lot of the world, they share stories, sometimes they complain about Bruce being Bruce together. He can make her laugh, she makes him smile. She understands a lot of what he's going through, he makes her feel at home.

Occasionally he jokingly suggests that she should make an honest man out of Bruce. She winks and says she'd rather make an honest man out of him. (Or any other way of getting them together, I just realised I ship them apparently. :D Just something friendly and gentle and good for both of them.)