Yup, that sure does sound like an open ground.
Here's a wiring diagram for an SB-2. You can click the image for a suitable-for-printing PDF.
Ignoring the bridge pickup, this shows how the split pickup is wired to the volume control. You may have a tone pot in there, but that's a separate deal.
You didn't mention whether or not the bass actually works, despite the hum. Your symptoms tell me that there is a break in (probably) the ground lead from the EA pickup or perhaps it isn't soldered as well as you think. Wiggle the ground wire going to the EA pickup along its length to possible find a break. Be careful as you get close to the pickup itself.
If you have no output from the pickup at all, also check the white & green leads and their connection to each other.
If the pickup covers lift off easily, you can visually inspect where the leads connect to the coils. If one is broken off here, it can usually be re-soldered.
Just remember that it is VERY easy to break a coil wire here, so be careful! This is the voice of experience talking, as I just had to have a pickup repaired for this very reason. And I'm pretty good with a soldering iron.
Ken...