The button is one of several varieties of Virginia State Militia buttons. Yours is shown as button VA-13 in the book "Record Of American Uniform And Historical Buttons" by Alphaeus H. Albert. Yours is a 2-piece button, so it was not worn by officers, who wore 3-piece buttons. Although VA-13 buttons have been found with many names as the backmark, all VA-13 buttons were made by the Scovill Manufacturing Company of Waterbury CT, from 1850 to early-1861, when Virginia seceded from the US. No VA-13 buttons are listed in the Albert book as having been made after the civil war.
Sorry, but unlike your VA-13 button, the bullet is definitely from sometime in the late-1800s or 1900s.