The 20-year-old will remain with the Championship club following a clutch of injuries to defenders at Ashton Gate.
The Robins were already without Louis Carey, Liam Fontaine and Jamie McAllister before Steven Caulker`s loan from Tottenham was cut short by a season-ending knee injury last week.
Spence has made four appearances during his initial one-month spell.
West Ham have a 24-hour recall option for the remainder of the deal.
Source: PA
Source: PA