Breezie posted one here that looks exactly like yours (also missing the base-plug) about a week ago. So, my answer is the same as I told her.
Your bullet is definitely an unfired civil war era Williams Type 3 "Bore-cleaner" bullet. The Type 3 made its first appearance on the battlefield in Summer 1863, and was used through the end of the war. All of the Williams bullets are .58-caliber, and all of them were strictly yankee-made. Here's a photo showing some Type 3 Williams bullets, with and without their base-plug (which some people call the "thumbtack" because it was a separate piece that was simply pushed into the bullet's base during manufacture).