The soldiers were told the bayonets were to remain in their scabbards and not attached to their service rifles.
Spc. Enrique Roman-Martinez's partial remains were found near Cape Lookout National Seashore.
The 64-page complaint was filed in the U.S. District Court for the Eastern District of North Carolina.
Col. Phillip Sounia was relieved of the command because of a "loss of trust and confidence in his abilities to command."
Fort Bragg was established in September 1918 as a place where the Army could do year-round artillery training.
The 10 bases in question include some of the largest Army posts: Fort Bragg, Fort Hood and Fort Benning.
The partial remains of Spc. Enrique Roman-Martinez were discovered after they washed ashore on May 29.
Intrusions make it harder for Fort Bragg to accomplish its mission and cost the Army money, officials say.
The officials said that about 200 soldiers with the 82nd Airborne's immediate response force will be the first to leave.
Some 1,600 active-duty soldiers are now staged just outside Washington, D.C. awaiting possible orders to support protest...