Owen Coyle’s side were awarded a penalty in the opening half which Martin Petrov converted.
Darren Pratley, who won the spot-kick, netted Bolton’s second in the 65th minute after meeting Robbie Blake’s cross.
Bradford threatened a revival as Nialle Rodney scored six minutes later but substitute Kevin Davies put the tie beyond the hosts’ reach by securing his third pre-season goal.
Ivan Klasnic completed the victory with a close-range finish.
“Over 90 minutes I was exceptionally pleased,” Coyle told reporters after the game.
“We scored four good goals and created a number of other goalscoring chances.
“We always looked a threat when coming forward which obviously bodes well for the start of the season.
“We knew that Bradford would be lively and that it would be a difficult challenge for us given that we’ve only just recently flown back from our successful tour of America.
“The squad are working well together and we can see the progress we are making as each day of our pre-season schedule goes by.
“We will be training again on Monday and Tuesday ahead of another tough pre-season game against Bury on Wednesday night.”
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Bradford City 1-4 Bolton: Owen Coyle hails pre-season progress