Have you tried doing a full expand on the tree?
After this use the inherited DrawToBitmap method.
You will have to perhaps behind the scenes, resize the control to show all items.
treeview1.ExpandAll();
treeview1.Size = new Size(600,850);
Bitmap bmp = new Bitmap(treeview1.Width, treeview1.Height);
treeview1.DrawToBitmap(bmp, treeview1.ClientRectangle);
Clipboard.SetImage(bmp);
Microsoft.Office.Interop.Word.Application wordApp = new Microsoft.Office.Interop.Word.Application();
wordApp.Visible = false;
object missing = System.Type.Missing;
Microsoft.Office.Interop.Word.Document wordDoc = wordApp.Documents.Add(missing, missing, missing, missing);
Microsoft.Office.Interop.Word.Range rng = wordDoc.Range(0,0);
rng.Paste();
wordDoc.PrintOut(missing, missing, missing, missing, missing, missing, missing, missing, missing, missing, missing, missing, missing, missing, missing, missing, missing, missing);
Tested and works great..