Neither side particularly troubled opposition goalkeepers but Rovers had the best of the possession.
The Rovers boss held his half-time team talk at the side of the pitch and made just the one change at the break as Adam Henley replaced Tommy Spurr. Former Rovers goalkeeper Matty Urwin was introduced for the hosts.
Paul Robinson dirtied his gloves in the second half as two dangerous and on-target shots from Mark Yeates and Alan Sheehan could have put Bradford City in front.
Luke Varney could have won it for the visitors in the final moments but he fired narrowly over from a tight angle to maintain the draw.
The game was used largely as an opportunity to test new talent, as Bradford made gradual substitutions throughout the second half and Rovers made nine changes at 70 minutes.
Bradford City manager Phil Parkinson said the result was an improvement for them and was pleased with how they coped facing a Championship side on home soil.
He told the club's official website: "It was a big step-up for us from the Shelbourne game and I felt we coped with it pretty well.
"I said leading up to the game that I felt we'd learn a lot more about ourselves after a match like this. It was a step-up today to play a Championship side like Blackburn and I felt physically we coped with the game quite well.
"We looked in good shape, which is obviously pleasing at this stage of pre-season.
"We still have two weeks of training to go (until the first game of the season) but physically I felt we looked in a good place.
"We know what we have to do to improve. Pre-season is a learning curve, especially when you bring in a group of new players, and we are learning all the time."
Bradford round off their pre-season at home to Hartlepool United on Saturday 2 August.
Rovers play their penultimate friendly this coming Wednesday night when they take on Bury at the JD Stadium before end their summer preparations at home to Stoke City on 3 August.