In her concession speech, Ms Bush declared: “All they did was radicalise me, so now they need to be afraid. Aipac, I’m coming to tear your kingdom down.”
Her fellow Squad member Jamaal Bowman, a two-term New York congressman, was defeated in a June primary.
Around $16 million was spent by Aipac and other pro-Israel groups on boosting his successful challenger, George Latimer, making it the most expensive primary in US history.
While most of the attack adverts deployed against Ms Bush did not explicitly mention Israel, Aipac dominated the race by spending around $9 million on advertising.
Congresswoman has denied spending allegations
The St Louis congresswoman has faced a number of challenges in recent months. There have been federal and congressional investigations into her campaign spending amid claims she improperly paid her husband, a security guard, for protection.
She has denied any wrongdoing and previously said the allegations were “simply false”.
Ms Bush’s defeat “is further proof that being pro-Israel is good policy and good politics,” United Democracy Project, an Aipac-affiliated group, said on Tuesday night.
The group vowed to “continue our efforts to support leaders working to strengthen the US-Israel alliance”.