Mrs Bercow, an outspoken Labour supporter, was invited to attend the service as the wife of her husband, John, who will be going.
But in a statement today, she said that she was not obliged to accompany him in the performance of his public duties.
She also accused No 10 of leaking details of her decision not to go to the press in order to try to undermine her husband.
"As Commons Speaker, John will be attending the funeral - and rightly so. But I'm not obliged to participate in my husband's public life - last time I looked, this was the 21st century! John holds public office and an important position, not me," she said.
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Feeling warm in this afternoon's sunshine. Breezy at times with the risk of an isolated shower.
Bright and breezy this afternoon with a few isolated showers around. Feeling warm in the sunshine.
Sir Bruce entertained audiences for more than seven decades.