Well, he's got the size for it, he probably played TE somewhere down the line and maybe he was just catching the ball a lot when they were messing around in practice.
On special teams it is necessary to catch and run with the ball. IE onside kick etc. I bet thats where it began. Or part of his experience in the past...
At that time, the Pats had Fauria, Fred Baxter and Cam Cleeland on the roster, so maybe having a defender jump in there seemed like a good idea. He did such a good job with it that, I imagine, he kept the position even after the drafting of Graham, then Watson.
Remember, before Dillon in 2004 the Pats were more of a pass-first team, so there were plenty of goal-line passes to go around (Fauria was another go-to guy).
I think I remembered hearing/reading somewhere that he was asked by Bledsoe to catch a few passes in warmups and then Drew put the "bug" into Bill's ear about using him as a TE. I'm pretty sure it was from an article if it means anything I could Lexis Nexis it later.