Democrats responded that Republican opposition to earlier plans to expand health care programmes made them poor advocates for the uninsured.
Nine members of Mr Bush's Republican party joined all 50 Senate Democrats to pass the bill, which gives patients wide powers to sue health insurers.
Mr Bush expressed disappointment with the Senate vote and said he "could not in good conscience sign the bill". He did not explicitly say he would veto it.
But the bill is popular with the public, and correspondents say that if debate drags on in the House, it could become an election issue in 2002.
Health insurers - known in the US as HMOs, or health maintenance organisations - mounted a $3 million campaign to fight the legislation.
Clash of interests
Mr Bush agreed with their stance that the bill "puts the interests of trial lawyers before the interest of patients".
Opponents of the bill argued in the Senate that it did nothing to protect people without health insurance.
Democrats responded that Republican opposition to earlier plans to expand health care programmes made them poor advocates for the uninsured.
Democrat Senator Edward Kennedy, one of three sponsors of the bill, said it would "protect patients and doctors, and end abuses by HMOs and managed care plans.
"Nothing persuades an HMO to do the right thing like the fear of liability if they do the wrong thing," he added.
His co-sponsors included Democratic Senator John Edwards - a former trial lawyer - and maverick Republican Senator John McCain.
Doctors versus insurers
The American Medical Association, a doctors' organisation, supported the bill.
The American Association of Health Plans, an insurers' group, opposed it.
Although passage of the bill was decisive and swift - Senate Majority Leader Tom Daschle pushed it through in two weeks - Democrats did not get the two-thirds majority they would need to overturn a Bush veto.
Thirty-five Republicans voted against the measure.
So did independent Senator James Jeffords, whose defection from the Republicans gave the Democrats control of the Senate - and the ability to push the bill through.