Town goalkeeper Marton Fullop single-handedly denied the hosts with a series of great saves, thwarting Arsenal loanee Jay Emmanuel-Thomas on three occasions as well as Peter Whittingham and Michael Chopra.
Whittingham saw his free-kick hit the crossbar while centre-back Dekel Keinan's first-half header was also ruled out for offside.
And Paul Jewell's side, who gave a good account of themselves despite struggling to create opportunities, showed Cardiff how it is done in style in the 67th minute as Bullard drilled a low effort past helpless debutant Stephen Bywater after good closing down from former Swansea striker Jason Scotland.
And the on-loan Hull man added a super second from distance four minutes from time, although his strike appeared to take a deflection.
Town's fifth consecutive victory over Cardiff leaves the Welsh outfit in third place having failed to capitalise on earlier results. Defeats for fellow promotion contenders Swansea and Nottingham Forest and
Norwich's home draw with struggling Preston made it a very good day for leaders QPR.
The Bluebirds started brightly with plenty of sharp passing amid an open beginning to proceedings in the evening kick-off.
And Fulop had to be on top of his game early on to parry Whittingham's 25-yard drive before getting back up quickly to turn Chopra's follow-up around a post.
The majority of the 21,347 present celebrated what they thought was a Cardiff breakthrough after 19 minutes only for Keinan, who capitalised on some slack Town marking, to see his header ruled out for offside.
City's interchanging attacking play was causing plenty of problems but Ipswich were also in the game and Bullard's free-kick stung the hands of Bywater amid a spell of pressure prior to the half-hour mark.
Town defender Mark Kennedy, who swapped Cardiff for Ipswich last summer, was forced off due to a hamstring strain in the 29th minute.
And Fulop was soon called to the rescue again to tip Emmanuel-Thomas' shot around a post.
The impressive keeper was beaten in the 31st minute but Whittingham could only watch in agony as his free-kick clipped the top of the crossbar.
But it did not take long for the Hungarian stopper to deny the hosts again, using his feet to block from Emmanuel-Thomas before Whittingham drilled wide in first-half injury time.
Fulop continued where he left off at the start of the second half, producing another great reflex save to keep out the busy Emmanuel-Thomas yet again, before he denied Chopra from the resulting corner.
And his saves proved crucial in the 67th minute as Bullard lashed a great strike into the bottom corner from 25 yards after some impressive pressing from Scotland.
The goal knocked the stuffing out of Cardiff, who failed to create another chance of note.
And Bullard doubled his tally for the afternoon from distance in the 86th minute, before coming close to a hat-trick with an 18-yard effort which forced Bywater into action.