IT IS horrifying enough that more than 100 women and girls may have been abused by a single USA Gymnastics doctor. It is more horrifying still that Larry Nassar was likely one among many. The widespread abuse of female athletes at USA Gymnastics came into the spotlight last summer after an investigation by the Indianapolis Star. Now, Sen. Dianne Feinstein (D-Calif.) has introduced a bill to close some of the loopholes that let it happen.

For at least a decade, Dr. Nassar, the subject of congressional testimony last month from high-profile gymnasts, passed off vaginal and anal penetration as treatment for back pain and other muscular maladies. Some did not realize they had been abused until they read related news coverage. Others had brought their concerns to parents and other adults and been told they were wrong — that the acclaimed physician, described as “a god to the gymnasts,” was only trying to heal them. Dr. Nassar has denied any wrongdoing.

Dr. Nassar is just the latest in a line of USA Gymnastics staff who used their authority to abuse. The Star reported in August that USA Gymnastics had complaint files on 54 coaches from 1996 to 2006 who may have assaulted gymnasts as young as 10. Since then, many more women have come forward with their stories. The scourge isn’t limited to USA Gymnastics: USA Swimming and USA Taekwondo have also been the subject of recent lawsuits.

Organizations such as these have failed to forward abuse complaints to law enforcement in part because they have no federal duty to do so. Ms. Feinstein’s bill would change that by establishing a nationwide reporting rule for amateur athletic governing bodies such as USA Gymnastics and the adults they authorize to interact one-on-one with athletes. It would also require the bodies to conduct stricter oversight of affiliate facilities, create easy mechanisms for making abuse complaints and track coaches who are the subject of complaints to keep them from moving to new states — and new athletes — when they get caught.

The U.S. Olympic Committee, which announced its support for Ms. Feinstein’s bill along with USA Gymnastics, will have to step up as well. The SafeSport initiative for independent investigations of abuse complaints is a good start. Its facility finally opened in Denver this year, and many of its objectives overlap with and would strengthen the provisions of Ms. Feinstein’s bill. The committee should also take it upon itself to decertify organizations that leave their athletes vulnerable to abuse and make them apply anew. It will take more than top-down actions from the Senate to reverse a culture that failed so many for so long, but at least Ms. Feinstein’s bill would write responsibility into law.