Ok, a couple of things.
First off, don't use the primary screen width - you can't show your PictureBox outside your Form, so use the form width instead.
Secondly, don't look for an exact match - check for "greater than or equal to" instead. Your way works fine when you increment by one, but if you decide to vary the speed, it could easily fail.
Then, to turn it round you are very, very close: all you need to do, is change your code very slightly, and move it around:
private void timer1_Tick(object sender, EventArgs e)
{
if (pictureBox1.Location.X >= Width)
{
pictureBox1.Image.RotateFlip(RotateFlipType.RotateNoneFlipX);
positionBird = false;
}
else if (pictureBox1.Location.X + pictureBox1.Width <= 0)
{
pictureBox1.Image.RotateFlip(RotateFlipType.RotateNoneFlipX);
positionBird = true;
}
if (positionBird)
{
pictureBox1.Left += 10;
}
else
{
pictureBox1.Left += -10;
}
}
(BTW: I moved the left hand side check, so the picture swaps over when it isn't visible)