A pair of senior lawmakers are proposing the first bipartisan legislation in the House this year to reauthorize the Export-Import Bank and impose new requirements intended to protect taxpayers.

Rep. Maxine Waters of California, the top Democrat on the House Financial Services Committee, and Rep. Gary Miller of California, the panel’s vice chairman, will propose Tuesday extending the bank’s charter for five years, while bolstering its risk and fraud protections, according to a copy of the bill reviewed by The Wall Street Journal.

“This legislation contains a responsible set of reforms that we believe will strengthen the Export-Import Bank and lay the groundwork for a bipartisan agreement that extends the bank’s charter over the long term,” Ms. Waters said in a statement.

The federal agency, which helps U.S. companies sell their goods overseas, has divided lawmakers. In September Congress extended the bank’s charter for nine months, through June 30, 2015, when lawmakers also voted to keep the government running until Dec. 11.

It’s not clear whether the lawmakers’ proposed changes to the bank would be enough to win over enough of its fiercest critics in Congress. Many conservative Republicans want to wind down the bank, saying it interferes in the free market and exposes taxpayers to too much risk. Critics of the bank, including the panel’s chairman, Rep. Jeb Hensarling (R., Texas), are expected to push for ending it next year, now that it expires on a separate timeline from the government’s funding. Mr. Hensarling indicated Tuesday he still intended to pursue shuttering the agency.

“With no further action or consideration expected during this Congress, I look forward to the bank’s expiration and working with members to make our exporters more competitive by advancing pro-growth tax, energy, regulatory and liability policies,” Mr. Hensarling said in a written statement.

Meanwhile, Democrats and some Republicans support extending the bank’s charter, saying it helps U.S. manufacturers and small businesses compete with foreign firms that receive similar aid from their own governments.

The draft legislation from Ms. Waters and Mr. Miller seeks to find some middle ground by combining a longer-term reauthorization with some measures intended to reduce potential risk from the bank’s loans and other assistance.

The bill would require the bank to allocate 50% of its net earnings each year to a “loan-loss reserve fund” until it has set aside enough money to cover 95% of the losses that could occur under a worst-case scenario. The bank’s default rate was 0.194% as of June 30 and the agency submits quarterly reports about its default rate to Congress.

The bank would also have to evaluate how well it is equipped to deal with employee misconduct and develop a policy for reporting fraud or corruption. Earlier this year, the bank suspended or removed four officials amid investigations into allegations of gifts and kickbacks, as well as attempts to steer federal contracts to favored companies, according to several people familiar with the matter.

The bill wouldn’t increase the bank’s $140 billion credit-exposure limit, instead asking the bank to publish a business plan within a year giving an estimate of the appropriate limits and whether they should be raised over the next two years. After the initial plan, the bank would be required to publish a business plan every two years. Earlier this year the administration proposed raising the bank’s exposure to $160 billion by 2018.

“The Export-Import Bank’s support of U.S. businesses is an example of how our government can facilitate job growth without adding to the national debt,” Mr. Miller said. In fiscal year 2014, the bank sent $675 million to the U.S. Treasury, money it earned from interest and fees.