"I will work across the aisle to put an end to this destructive pattern of behavior in Washington," she said. "If I don't do my job, you need to do your job and vote me out" and said Bishop also deserves such treatment.
McAleer lost to Bishop by a 72-25 percent margin last year but suggested things have changed.
"This is the second time in less than eight months that Bishop's votes have caused pain and suffering, furloughing civilian workers at Hill," noting defense workers faced a six-day furlough earlier this year because of sequestration.
She said an estimated 40,000 Utahns are out of work now because of the current shutdown and "are suffering because the government has sold them out to partisan politics."
Her announcement comes after another Democrat, Ogden physician Peter Clemens, announced last week that he will also seek the Democratic nomination against Bishop.
McAleer was president of her class at West Point, is a former second lieutenant in the Army, led the global division of the technology firm GenRad and was a world-class bobsledder who just missed qualifying for the Olympics in 2002. She is the former executive director of the People's Health Clinic in Park City and iauthor of the book "Porcelain on Steel: Women of West Point's Long Gray Line."