Every job I've ever had has had a rule against carrying weapons to work, and included the parking lot in the definition of "work." That's been a lot of years. Not one time in 40 something years, has an employer EVER asked to search my vehicle. I have never heard of any of my fellow employee's being asked to allow their vehicle to be searched. Not once.
I'd put the gun in the glove box and lock the doors and go on about my business. If you're worried that someone will break into your car, put a lock box in the car. Then lock the car and go on about your business.
Not asked? Don't tell.
Now if you happen to work for someone who routinely searches vehicles, take a different approach.
For God so loved the world, that He gave His only begotten Son, that whoever believes in Him should not perish, but have everlasting life.
John 3:16 (NKJV)