Lyncat,
Those "White / Kenmore" type bobbin cases are as simple as a Class 15 singer case. Don't over think them.
Hold it in you left hand open side up, with the little projection pointing up. Put the filled bobbin in the case with the thread coming up from the left side. Draw the string into the little notch to the left of the projection, then across and behind the bottom of it. (If you look at your pic you can see the notch just to the left - bottom of the projection.) Pull the thread up into the grove and between the spring and case. There is a slot on the back side of the spring for the thread to pass through. This is what controls the tension.
Once the bobbin is threaded into the case it should rotate clockwise when you pull on the thread.
If you need I can do a couple pics to help.
Joe