Saltonstall has played in all three of Bradford's pre-season friendlies and the 20-year-old will now remain in West Yorkshire for the start of the Super League season.
"We are really pleased to see James staying around for another month, he is a great guy to have around the place," said Bulls head coach Francis Cummins.
"He has worked extremely hard since he arrived and he has certainly put himself about while on duty in the trial games.
"James will be continuing training with the first-team squad, upping the competition levels out wide while adding further pressure for places."
Wolves boss Tony Smith added: "At the moment we are happy for James to stay at Bradford, until we look at things further down the line.
"We will be working out what is the best spot for him, either at Bradford or back with ourselves, but we will certainly look at that in the coming weeks."
Saltonstall was born in Halifax, but he represented Italy at last year's World Cup.