I ran his name through the database for Canadian WWI soldiers, thinking that he may have signed up a second time when the Great War broke out, but no luck. Someone else I was researching was veteran of the Boer War and his WWI papers gave an impressive overview of his Boer War experiences.
There was a "William Thomas" Bull, but he was far too young to have served in the Boer War.
At least you know that source of information came up empty.