How old is Bruce/Batman supposed to be?

Before anyone answers, I get comicbooks operate on a floating timeline and no one ever actually ages. However it still feels strange that Bruce knew Dick Grayson, Jason Todd, Barbara Gordon, Tim Drake, and Damian when they were kids or teenagers and now most of them have entered adulthood; but Bruce hasn’t really changed.

It reminds me of Magneto from Marvel where he was a victim of the holocaust, but that was 80 years ago and he’s somehow still alive.