Any particular reason you're not reading the value of the checkbox using the name of the checkbox itself?
If the range defined by your bookmark contains a checkbox, then, depending upon how the checkbox is inserted, it will be found in either the InlineShapes
collection (if checkbox inserted inline with the text) or the Shapes
collection (if inserted as a floating object.)
You would then need to iterate through the collection of Shapes or InlineShapes looking for the checkbox in question.
Iterating through controls in InlineShapes collection
Dim ctl As InlineShape
For Each ctl In rng.InlineShapes
If ctl.Type = wdInlineShapeOLEControlObject Then
If ctl.OLEFormat.ClassType Like "Forms.CheckBox*" Then
'current version of ctl is a checkbox, do what you will with it.
End If
End If
Next ctl
...
This ought to get you closer, but if the name of the checkbox is predictable, it is better to address it directly by name.