Bullingham spoke as The FA joined nine other European federations in supporting a season-long OneLove anti- discrimination campaign.
Some LGBTQ+ England supporters are not travelling to the Muslim-majority nation where same-sex relationships and the promotion of same-sex relationships are criminalised.
An Enabling Law is planned in the Arab state meaning minor offences won’t be prosecuted.
Rainbow flags will be allowed at games as long as they are not draped inappropriately, the FA chief insisted.
Bullingham said his organisation was also lobbying the game’s global governing body FIFA for an update regarding a compensation scheme for migrant workers who helped build stadiums and infrastructure in Qatar.
Amnesty International called upon FIFA to establish a fund of at least £350 million for workers who have suffered “human rights abuses” – a sum is equivalent to the prize pot for the World Cup. It comes amid reports some were paid just £12 to work 11-hour shifts.
Asked what his advice was to gay England fans planning to travel, Bullingham told reporters on Wednesday: “We understand that concern. I understand quite a few of them won’t be going out.
“The message we’ve have really clearly from Qatar, overall, is everyone is welcome and those communities are absolutely welcome.
“We’ve asked the question in lots of meetings, whether it’s with the security teams on the ground, and they all certainly give the right answers. There’s still some more information needed. What does accommodation look like and so on?
“Those [LGBTQ+] communities have been clear they haven’t got all of the information they need to make that decision yet.”
Bullingham when asked if he felt the Qataris could go further in promoting human rights added: “If you look at LGBTQ rights, there are deep-rooted, societal, cultural and religious beliefs that are very unlikely to change anytime soon.
“So I think the approach there has been to welcome people. I don’t think we’re expecting significant changes in the legislation related to those communities.
“I have found with regards to human rights, construction rights and workers’ rights absolutely a desire for change. That’s not every single person you meet. I think the authorities have been really sincere about the changes they have brought about.
“When they talk through it, they are quite proud actually of what they have done in such a short space of time. It’s from a low base.”
On Wednesday, it was announced England captain Harry Kane and the captains of the eight other countries who have qualified for the World Cup will wear the OneLove armband in Qatar.
Kane will put his on for the first time in Friday night’s Nations League match against Italy.
Kane said: “I am honoured to join my fellow national team captains in supporting the important OneLove campaign.
“As captains we may all be competing against each other on the pitch, but we stand together against all forms of discrimination.
“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.”
The FA said a group of migrant workers had been invited to England’s World Cup training base at Al Wakrah to meet the players.
Amnesty welcomed the FA’s stance on discrimination and migrant worker rights.
The organisation’s head of priority campaigns, Felix Jakens, said: “The FA’s pledge to support efforts to remedy abuses suffered by thousands of overseas workers in Qatar – including with a Migrant Workers’ Centre – could be significant, but we still need to see whether this is seriously taken up either by the Qatari authorities or by FIFA.
“Human rights issues have plagued preparations for this World Cup, and we’ve previously been disappointed by years of FA reticence and over-optimistic statements about ‘progress’ in Qatar.
“Unexplained migrant worker deaths, workers being cheated of their wages and others working extremely long hours are just some of the issues that Qatar’s patchily-enforced labour laws are still failing to address.
“Top-flight football is immensely rich and genuinely influential, and FIFA should have insisted on human rights clauses when it originally assessed Qatar’s hosting bid.”