First time I'm hearing of this recessive white, gene DNA test. Hopefully they come out with other color mutation DNA tests as well.Breeding her to her own son would work equally well as a test for recessive white. It just takes longer (need to raise a son to adulthood, as compared with using her father who is already an adult.)
Yes, I can see why you would want to keep recessive white out of your flock of BBS.
If you want to be sure your BBS flock has no recessive white, you could test-mate every bird involved (breed each one to a recessive white, hatch enough chicks to either find a white one or be reasonably sure they will not produce any white ones.)
Oh, I just remembered, there is now a test for recessive white:
https://iqbirdtesting.com/whitegene
Testing one bird (the puzzling pullet) might be cheaper than test-mating, by the time you consider the feed & time involved.
They can test a sample of blood or feathers (or eggshell, but that would mean the shell she hatched from: I'm guessing you no longer have that.)
If she has recessive white (confirmed by test mating or a DNA test), I would be suspicious of any other chicks that originated in the same flock. If she does not have recessive white, there is no real reason to suspect any of the rest would have it either.
That does sound like it will give you quite a variety of chicks!