Same-sex sexual activity is illegal in the Gulf state, raising concerns within the LGBTQ+ community over how safe they will be at the finals this winter.
Bullingham says he has been told some fans from the community will stay away because they have simply run out of time to receive adequate assurances around accommodation.
But he said police in Qatar had been briefed to be tolerant during the tournament.
Asked whether the FA had planned for the scenario of an England fan being arrested for holding hands or kissing a same-sex partner in public, Bullingham said: “We have been asking those questions of the Qatari authorities over the last six months.
“They have absolutely told us all the right answers for anything we’ve talked about, even down to the point of ‘are rainbow flags allowed?’
“Yes, absolutely (they are allowed) as long as someone doesn’t go and drape them on the outside of a mosque – that was one example we were given – and were disrespectful in that way.
“But they have absolutely been briefed to be very tolerant and act in the right way. Any time we ask a direct question we tend to get an answer.”
However, the FA continues to request more detail on the assurances given by the local organising committee that all fans, including those from the LGBTQ+ community, will be welcome, safe and secure in Qatar.
The FA has joined nine other European federations in joining the OneLove anti-discrimination campaign. As part of that, England captain Harry Kane will wear an armband supporting the campaign at the finals this winter, along with the skippers of the eight other European nations signed up whose teams have qualified.
“As captains we may all be competing against each other on the pitch, but we stand together against all forms of discrimination,” Kane said.
“This is even more relevant at a time when division is common in society. Wearing the armband together on behalf of our teams will send a clear message when the world is watching.”
Bullingham said his organisation was also lobbying the game’s global governing body Fifa for an update regarding a compensation scheme for migrant workers in Qatar and the creation of a centre to help those workers access support.
“We continue to push for the principle of compensation for the families of migrant workers who have lost their lives or have been injured in construction projects,” he said.
“Again, we are pushing Fifa for an update on the compensation fund which has been consistently referenced as a safety net where workers and their families have been unable to secure compensation from the construction companies.”
Human rights organisations including Amnesty International have called on Fifa to set aside 440 million US dollars (£388m) to support a compensation fund and help establish a migrant workers centre.
The amount is equivalent to the prize money on offer to teams at the World Cup.
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