The Gulls skipper was sent off after 35 minutes at Valley Parade for an alleged elbow on City left-back James Meredith.
Boss Martin Ling said: "Brian is not that kind of a player and I am going to look at the video to see if we can appeal against his dismissal."
Ling admitted that Torquay rarely threatened in attack, but added: "We were unfortunate when Naill Thompson hit the post in the first half.
"The cross that led to Bradford's winner was the result of a poor cross and there were chances to clear the danger. We defended all the quality crosses that went in superbly."
- Sports & Recreation