Ms Abbott said that in the course of this week’s programme, recorded in Derby, she was interrupted more than double the number of times Tory MP Rory Stewart was, and was not allowed to respond to a “blatantly abusive remark” from the audience.
She said she had also been told Ms Bruce had made unpleasant remarks about her to the audience before filming began and the audience had been “wound up” against her.
In a statement, the BBC denied that any of panellists on the programme had been treated unfairly.
Writing for the Independent, Ms Abbott said: “Over a long political career I have appeared on BBC Question Time innumerable times, but I have never had such a horrible experience as I had in Derby last week.”
In one exchange about letters sent between Labour leader Jeremy Corbyn and Prime Minister Theresa May following the Brexit vote, Ms Bruce asked her: “Why don’t you just talk?”
In another exchange with the journalist Isabel Oakeshott about whether Labour or the Conservatives were ahead in the polls, Ms Abbott said they were “kind of level pegging”.
Ms Bruce then interrupted to tell her: “You are behind, Diane.”
In her article, Ms Abbott said unlike the programme’s previous host, veteran broadcaster David Dimbleby, Ms Bruce did not appear well-briefed and had got the polling wrong.
“She (or her researcher) appears to have got their figures from a Conservative Central Office handout. Above all, it seems she is not afraid to appear unfair as a presenter,” she said.
She said the BBC needs to start treating Mr Corbyn and his ministers as “legitimate political actors” and accord them the same respect they give to Tory ministers and MPs on the Labour right.
“It would be wrong to blame Fiona Bruce for all this. Question Time has had a new editor for some time, and seems more interested in entertainment than politics,” she wrote.
“In the current abusive political climate, TV production teams need to reflect before they wind up live audiences against particular politicians. It may result in ‘good television’, but it can easily turn ugly.”
Ms Abbott said she is not asking for “special treatment, only fair treatment”.
She added: “Many viewers and people in the audience for last week’s Question Time thought that the way I was spoken about before the programme, the way that I was treated during the programme, and the chairing of the programme were decidedly unfair.”
In a tweet, the BBC news press team said that while a YouGov poll on the day of the programme put the Conservatives ahead, Ms Abbott was right to say other polls suggested Labour was either ahead or tied.
“We should have made that clear,” it said.
A BBC spokesman said: “We are sorry to hear Diane Abbott’s concerns over Thursday’s edition of Question Time and we have contacted her team today to reassure them that reports circulating on social media are inaccurate and misleading.
“Diane is a regular and important contributor to the programme. As we said earlier, we firmly reject claims that any of the panel was treated unfairly either before or during the recording.”