I can't really find any official/canonical/whatever-it's-called sources, but  [this random youtube video](https://www.youtube.com/watch?v=u0bTCeUUoP0) at 0:49 says he was "in his 50s", and page 64 of the the book *Modern Masters Volume 3: Bruce Timm* says he was 80:

> Bruce Wayne at age 80, as he appeared in *Batman Beyond*.
>
>([1](https://books.google.no/books?id=EMwn_4llWK0C&pg=PA67&lpg=PA67&dq=Bruce+Timm+kid-friendly+Batman+Beyond+cartoon&hl=en&redir_esc=y#v=onepage&q=60&f=false) , [2](https://scifi.stackexchange.com/a/100652/23918))

(also 80s looks way more likely to me than 50s, but I'm no expert)