Who won the Bull Run battle?
The Confederates (The South) won both the battles of Bull Run (or Manassas, as the South likes to call them.)
The first was won by Joseph E. Johnston and P.G.T. Beauregard, over the Union commander Irvin McDowell.
The second was won by Robert E. Lee and T.J. ("Stonewall")
Jackson, over the Union commander John Pope.
The Confederates - both times.