Thanks to this thread I got out an old tape of Paddy Tunney, who is the acknowledged source of most of the people who sing this song, and he definitely sings beagle rather than beadle. As to pronunciation he doesn't pronounce it exactly like bagle, but the first syllable definitely sounds closer to Bay than to Bee.

Anyway its nice to get an excuse to dust off the old tapes and have a listen every now and again.