Yeah, Bradfords aren't supposed to be fruit-bearing.

Our Brad's just a skinny, skanky stick because it was
within a copse of fast-growing hybrid poplars depriving
t of light. In 2005, we removed the pops as they
were beginning to succumb to wind storms.

The Brad's still just a 15-foot stick, but for some reason,
either in gratitude for taking down the poplars, or perhaps
it had something to do with the drought March-August 2006,
ol' Brad produced about a dozen large pears. Most fell
to the ground hard and stayed hard.

However, two of them ripened nicely. They looked
identical to large Bartletts and were very juicy.
Quite sweet too, but with a slight tang.
______

Bradford Pears actually do bear fruit. It's about the size of a small
acorn and inedible. I don't think what you have is a Bradford Pear.
________

Curious, because I paid for a Brad and the flowers every year have
been showy, notwithstanding the tree's small stature.

About 50 yards away, I have a Bartlett pear, grown from seed in 1979,
and now 40 ft. tall.

Maybe the two had sex and the Bartlett's genes dominate the babies.