I think you're confusing terms--dominant means that it takes precedence over other alleles. In this case, if the bird is (B,b) or (B,B), the bird will be barred. Only if (b,b) will the bird not be barred. This is a sex-linked gene as you indicated, and females only have one copy. A hen who is (B,-) will be barred and one who is (b,-) will not.
For sex linked genes, dominance doesn't matter in the hen as there can only be one copy; nevertheless, the B allele is still referred to as dominant. Kind of like red is still red, even if you're looking at a black and white photo of something that is red.
You are correct that hens can only pass the gene to their sons, so perhaps I wasn't clear when I said that it didn't matter which parent it was inherited from. Perhaps if I rephrase it to "barring inherited from the mother looks no different than barring inherited from the father." Barring inherited from both parents does look different than barring inherited from only one. In this case, the white bars are wider, making a lighter coloured bird.
The male offspring of a barred roo crossed to a non-barred hen should look the same as male offspring of a non-barred roo crossed to a barred hen, at least as far as barring goes.