A bipartisan group of senators is criticizing the Consumer Financial Protection Bureau’s effort to combat alleged discrimination in the auto-lending market, saying the regulator hasn’t shown enough evidence that problems exist.

The 11 Republicans and 11 Democrats, led by Sens. Rob Portman (R., Ohio) and Jeanne Shaheen (D., N.H.) sent a letter to CFPB Director Richard Cordray Wednesday asking for details on how it analyzes auto loans for potential discrimination against minorities or women. The topic is a priority for the bureau. As a way to avoid discrimination, it has pushed to standardize or limit interest-rate charges added by auto dealers.

The bipartisan criticism is a major challenge to the new regulator, created under the 2010 Dodd-Frank financial law to police the financial system for consumer abuses. Until now, criticism of the agency has been largely confined to Republicans who opposed the bureau’s creation.

In March, the CFPB told lenders they must do more to ensure that car loans comply with laws barring discrimination against minorities and women. Auto dealers, who arrange financing for most car buyers, say there is no evidence of discrimination and have been up in arms about the CFPB’s effort.

Dealers are a powerful lobby on Capitol Hill, and won an exemption from the bureau’s oversight more than three years ago. Still, the bureau has broad authority over the lending industry.

In a recent speech, CFPB Deputy Director Steve Antonakes referred to the March guidance, saying: “Earlier this year, we made it clear that we have the authority to pursue auto lenders whose policies harm consumers through unlawful discrimination.”

A CFPB spokesman did not immediately comment on the letter.

In the letter, the senators asked why the CFPB warned auto lenders about the discrimination issue without an official rule-making process, and whether it conducted a cost-benefit analysis of changes to the auto lending market.

In a statement, Mr. Portman said he is “concerned about the Bureau’s lack of transparency and unwillingness to make public the basis for its policy decisions, especially those that could negatively impact competition and consumers.” Ms. Shaheen said the CFPB’s discrimination guidelines “could restrict legitimate credit options and increase costs for many Americans looking to finance their cars.”

Dealership owners from around the country recently traveled to Washington to press lawmakers on the issue and defend the industry’s loan pricing system, which they argue allows consumers to receive discounts from what banks would otherwise charge.

Bailey Wood, senior director for legislative affairs at the National Automobile Dealers Association, said the CFPB needs to be more open about its analysis. “If a government agency is hiding their statistics and methodology, it means it doesn’t have to stand up to public scrutiny,” he said.