I believe the jug was part of his family crest. I've attached the crest below.

Stephen

Mark Williams wrote:

Over on the classics list we've been having a little discussion about the
venerable Bede who is often portrayed in art with a jug (looks kind of
like a beer-stein, according to one participant in the thread).  Is it
common to portray Bede in this way?  What is the iconography or
significance of the jug (if any)?  I know nothing about this.