The huge majority of women in Congress are Democrats anyways. Have them put out a statement saying "Speaker Johnson. The undersigned women in Congress who use these restrooms welcome Rep. Elect McBride in our facilities. You can keep your meddling hands out of regulating out bathrooms the same as you can keep your meddling hands out of regulating our uteruses.
If you were truly interested in keeping the women of Congress safe from men, the Ethics committee could choose to respond to the XX sexual harassment and assault complaints filed against currently sitting congressmen that have gone nowhere.