Saving to an image isn't really viable for what it sounds like you want to do because restoring vector lines from a bitmap is much harder and potentially lossy than the vector to bitmap conversion, in addition to not being very efficient from a data density perspective.
You could write some code to save and restore the collection of lines that's stored in the Strokes property. This would allow you to reduce the size of your data down to a minimum and easily store in a database. Each Stroke has some data about what the line looks like and a set of points that make up the line. It's fairly simple to extract and restore that data to another InkCanvas when reloading.
You might also be able to use XamlWriter/XamlReader to just serialize the entire InkCanvas to xml but you would need to be able to put the new deserialized instance into your UI and make sure there aren't any naming or resource complications in your XAML that tend to cause errors with this method.