A check of the 1901 census finds:
Albert Bibb Parents John H & Mary A Born Abt 1886 Birmingham Son Residence Aston Manor
Albert G Bibb Parents George Mary E Born abt 1889 Birmingham Son Residence Birmingham
So there is certainly two of them
I think it may be a second marriage for George as the census records:
RG13; Piece: 2846; Folio: 107; Page: 6
Address: 4 Court 7 house Charlott? Street, Birmingam
George Bibb Head M 36 Shell ? Maker Warwick Aston
Mary E Bibb Wife M 25 Warwick Birmingham
Marion Bibb Daur S 10 Warwick Birmingham
Albert G Bidd Son S 12 Warwick Birmingham
This would make Mary 13 when she gave birth to Albert. Possible of course.
Unfortunately I cannot pick them up in the 1891.
Doug