The Case needed will depend both on the Bass you have and the type of extension you are installing.
I have a fairly large 7/8 Bass with a custom made C-ext. by Arnold Schnitzer. It only sticks up about 1 1/4" over the top of the Scroll. I have a regular 7/8 size case and it fits fine. The newer Chinese type cases called 4/4 or full sized also fits but are kinda snug because of the wider bouts and deeper ribs of my older Bass.
Heres the pics;
http://www.kensmithbasses.com/Double...orelliBass.htm
Years and years ago, I had a 3/4 Wilfer Bass and had a Mechanical Ext. installed. I ordered a custom case as the 3/4 was too short and the 7/8 was too big on the body.. Like I said, it depends......