Found the answer is:
Me.ClientSize = New System.Drawing.Size(img.Width, img.Height + ToolStrip1.Height)
To resize while maintaining the aspect ratio the code is:
Dim ratio as Double
Private Sub Form_Shown(sender As System.Object, e As System.EventArgs) Handles MyBase.Shown
Dim img As Image = Image.FromStream(New MemoryStream(File.ReadAllBytes(_filename)))
PictureBox1.Image = img
PictureBox1.SizeMode = PictureBoxSizeMode.Zoom
Image_ratio = img.Height / img.Width
Me.ClientSize = New System.Drawing.Size(img.Width, img.Height + ToolStrip1.Height)
Me.Activate()
AddHandler Me.Resize, AddressOf Form_SizeChanged
End Sub
Private Sub Form_SizeChanged(sender As Object, e As EventArgs)
'Resize while maintaining aspect ratio
Me.ClientSize = New System.Drawing.Size(PictureBox1.Height / Image_ratio, Me.ClientSize.Height)
End Sub