Argyle started brightly with Andres Gurrieri going close from Reuben Reid's cross from the right but it was thanks to keeper Jake Cole they were still level after eight minutes.
Plymouth's number one made a brilliant one-on-one save to deny Garry Thompson after the Bradford striker skipped the home side's offside trap.
The save spurred Argyle on and on-loan Crystal Palace striker Jason Banton forced City keeper Matt Duke into a full length stop to keep out his 24th minute angled drive.
Duke found the shot too hot to hold and Gurrieri's follow-up strike needed to be cleared off the goal-line by Bradford left back Carl McHugh.
Cole made a routine save to keep out Kyel Reid's free kick but Banton was by far the liveliest forward and came closest to breaking the deadlock early in the second half.
Banton beat Duke with a thumping angled drive from the left but watched his 10-yard strike smash off the upright.
It was then Thompson's turn to rattle the woodwork with a thumping volley from 20 yards with time running out as both sides had to settle for a point.
