I don't know if it's modesty or just didn't seem lady-like to her

But I for one think it's one classy thing for a woman to have done for her country during World War II:

Hoo-rah! Bea Arthur was a truck-driving Marine: Documents say actress served her country during WW II, but she denied it in 2001

Bea Arthur served up the jokes, making America laugh for decades on TV – but, as it turns out, the late actress also served her country in the Marine Corps during her youth.

According to TheSmokingGun.com, the “Maude” and “The Golden Girls” star served for 30 months starting in 1943. She reportedly was a member of the Women’s Reserve and worked as a truck driver and typist.