Private businesses can ban guns if they wish to.
Private businesses cannot ban employees from keeping guns locked in their cars.
Are you describing Arizona?
Here in the People's Republik of Kalifornia I am sure that employers may ban employees from keeping guns locked in their cars. My employer of many years was careful to state that there would typically be no need to look into people's cars, but the employer reserved the right to do so on their property.
Should a search take place and a firearm be found, it was grounds for dismissal. My employer did not have a policy forbidding having a "Life Member of the NRA" vanity license plate displayed in my cubicle.