Copy a rectangluar portion of Bitmap using LockBits

I'm using the following code to lock a rectangle region of a bitmap

    Recangle rect = new rect(X,Y,width,height);
    BitmapData bitmapData = bitmap.LockBits(rect, ImageLockMode.ReadOnly,
                            bitmap.PixelFormat);

What seems to be the issue is bitmapData.Scan0 gives me IntPtr of the top left corner of the rectangle. When I use memcpy, it copies the contiguous region in memory upto the specified length.

memcpy(bitmapdest.Scan0, bitmapData.Scan0, 
             new UIntPtr((uint (rect.Width*rect.Height*3)));

If following is my bitmap data,

a b c d e
f g h i j
k l m n o
p q r s t

and if the rectangle is (2, 1, 3 ,3) i.e, the region

g h i
l m n
q r s

using memcpy gives me bitmap with the following region

g h i
j k l
m n o

I can understand why it copies the contiguous memory region. Bottom line is I want to copy a rectangle region using Lockbits.

Edit: I used Bitmap.Clone, but it was faster when I flipped the Y (less than 500ms)

bitmap.RotateFlip(RotateFlipType.RotateNoneFlipY);

but it was very slow when I didn't flip Y (30 seconds)

Image size used was 60000x1500.