Sheila Bair, former chair of the FDIC, wants to fix the student debt crisis — and she thinks Democratic presidential hopeful Elizabeth Warren has some "bold" ideas that may work.

Warren, a Massachusetts Democratic senator, announced her plan to wipe out student debt and public college tuition earlier this week.

"I have some different ideas on this but … she's got something bold, dramatic, she pays for it and she's tackling a core problem," Bair said Wednesday on "The Exchange."

"This debt overhang we have now is a big drag on the economy," Bair added.

Americans owe $1.57 trillion in student debt. Warren claims her plan will cancel at least some of the debt held by 95% of the Americans carrying it.

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She proposes eliminating up to $50,000 in student debt for those with household incomes under $100,000, which would cost $1.25 trillion. She would also allow states to make public colleges tuition-free and wants to spend $100 billion on extended Pell Grants to help with nontuition costs.

Warren would pay for it with her wealth tax of 2% on those with a net worth between $50 million and $1 billion. A 3% tax would apply to household net worth above $1 billion.

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While some may disagree with the idea of a wealth tax, Bair said at least Warren is trying to fix the problem in a "fiscally responsible way."

Bair, a member of the CNBC Financial Wellness Advisory Council and former president of Washington College, has her own ideas on how to address student loan debt.

She would restructure the system so students don't have any debt. Instead, Bair proposes an income share that would see a financier and student singing a contract that has the student pay a certain percentage of his or her income over a certain period of time, subject to a cap. She has called the percentage "affordable" and said it would only kick in once the now-graduated student has a "decent" income."

— CNBC's Tucker Higgins and Jacob Pramuk contributed to this report.

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