Mr Jarvis said it would be "a bit of a trial and error" process to begin with but it was likely only one person would be armed at any one time.
That person would be in radio contact with team members stationed at either end of the bridge who would control traffic while shooting was taking place.
While this method would be slightly more expensive than the poison option, it would have a higher success rate.
However, "I would be surprised if we got the whole lot".
A reduction in numbers though will allow the agency to clean excrement from the bridge to assess the damage.
Mr Jarvis said the excrement was corroding the structural steel of the bridge and while it was not an immediate safety risk, they needed to reduce pigeon numbers now in order to repair the bridge.
Depending on how this operation went, another one may be required in a years' time.
It has been 25 years since the population had been targeted and if left another 25, there would be serious issues with the bridge, he said.
The work is expected to take several weeks though bad weather could prolong it.