Hi - A US 1890 census might not have helped. In the 1911 census Bernard was with his family in West Derby Lancs aged 17 (b. New York, USA), as was his sister Margaret aged 19 - born Liverpool - as were his younger siblings aged 10 and 6.
So their mother seems to have been in Liverpool until 1892, and back there before the 1901 census. The 1901 census also had son John aged 5 b.Liverpool (but same place was put for all the children). It was only in the 1911 census which mother Bridget seemed to make a point of writing New York USA for son Bernard, and also that he was a British Subject by parentage.
No sign of John with the family in 1911.

Sue