You'll get better performance and automatic conversion to splines (if you want it) by using an InkCanvas instead:
<InkCanvas>
<InkCanvas.DefaultDrawingAttributes>
<DrawingAttributes Color="Blue" Width="8" Height="8" FitToCurve="True" />
</InkCanvas.DefaultDrawingAttributes>
</InkCanvas>
You can always get it to render itself into a bitmap later if you need it:
RenderTargetBitmap bitmap = new RenderTargetBitmap((int)theCanvas.ActualWidth, (int)theCanvas.ActualHeight, 96d, 96d, PixelFormats.Default);
bitmap.Render(theCanvas);
UPDATE: this works for transparent brushes as well BTW, and also pressure-sensitive pens (if enabled). The main problem is that the performance will drop as the user draws more and more lines, but you can easily fix that by rendering to a bitmap and then setting that bitmap to be the InkCanvas background i.e. the InkCanvas shouldn't never be displaying more than 1 spline, and only when the user is drawing it.