I want to use the GDI+ drawing in my WPF control.
Try compositing a Windows Form User Control in your WPF project and encapsulate GDI+ drawing in it. See Walkthrough: Hosting a Windows Forms User Control by Using the WPF Designer
WPF comes with new graphics features, you can investigate it here, but if you want to use an old GDI+ API one way to do is to create Winform draw there and host it into WPF
This is generally a bad idea. WPF is a completely new API and mixing in GDI+ may result in poor performance, memory leaks and other undesirable things.
There are several ways to do this, the easiest would be to lock your Bitmap you manipulated with GDI, get the pixel buffer (Scan0 IntPtr in the BitmapData you get from the lock). CopyMemory(...) from you pixel buffer to a WriteableBitmap.BackBuffer.
There are more performant ways in WPF, like using the InteropBitmap instead of WriteableBitmap. But that needs more p/invoke.