Two loops: (I'm sure I'll get this wrong.)

  for (int ii = 0; ii < n-1; ++ii) {
    // ii+1 largest elements end up in their correct position at the end of this loop.
    for (int jj = ii; jj < n-1; ++jj) {
      if (arr[jj] > arr[jj+1]) {
         swap(arr[jj], arr[jj+1]);
      }
    }
  }

One loop:

  int ii, jj;
  for (ii = 0, jj = 0; ii < n-1; ii = ((jj == (n-1)) ? (ii + 1) : ii), jj = ((jj == n-1) ? ii : (jj + 1))) {
    // compare and swap as before
  }

Unreadable, but it's one loop.

EDIT: use code formatting, oops. EDIT 2: add proper conditional for jj update instead of jj = jj + 1.