The 34-year-old actress, Heather Lind, wrote in a now- deleted Instagram post that she was standing next to the former president when he "touched me from behind from his wheelchair with his wife Barbara Bush by his side".
She said the incident occurred four years ago at an event to promote the TV series "Turn: Washington's Spies."
Lind also alleges that Bush, 93, told her a "dirty joke".
"President Bush would never under any circumstance
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intentionally cause anyone distress, and he most sincerely apologises if his attempt at humour offended Ms Lind," the former president's spokesman Jim McGrath said in a statement.
"President Bush has been confined to a wheelchair for roughly five years, so his arm falls on the lower waist of people with whom he takes pictures," the statement read.
"To try to put people at ease, the president routinely tells the same joke -- and on occasion, he has patted women's rears in what he intended to be a good-natured manner.
Lind, who starred in AMCs TURN: Washingtons Spies, wrote in the caption of her Instagram which featured a photo of former Presidents Barack Obama and Bush shaking hands in a gathering of other former presidents, that this image had "disturbed" her.
Bush served one term as US president from 1989 to 1993, and is the father of George W Bush, who served two terms in the office between 2001 and 2009.
He suffers from a form of Parkinson's disease.
Lind finished her post with the hashtag #metoo, which has seen widespread use by victims of sexual assault to share their experiences in the wake of the Harvey Weinstein Hollywood scandal.
"What comforts me is that I too can use my power, which isn't so different from a president really," she said.
"I am grateful for the bravery of other women who have spoken up and written about their experiences."
Another actress, Jordana Grolnick also accused Bush of inappropriate touching.
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