Before looking at exercises to strengthen your pinky, I'd look at your hands, your bass, and your technique. I'm not saying that your technique is bad or that you shouldn't do exercises aimed at increasing strength, flexibility, independence, and endurance -- improvements in any of those areas can only help. But they can only help to a very limited extent if your technique is in the way. At best, improvement will be marginal and slow. At worst, you'll get injured.
Again, not saying your technique is bad or that your pinky doesn't need dedicated exercise. I am saying that, based on your post, it's impossible to tell. The trouble-shooter in me says, "Check those other things first." How you hold your thumb and how you balance your hand on the fretboard, for instance, can make a difference in how far your pinky has to reach and how hard it has to work in general. (It's smaller than your other fingers -- don't put it in an unnecessarily disadvantageous position.)
Maybe you know all this, though.
Assuming your technique is sound (everyone's hands are different -- and I'm not saying there's only one "right" technique) and your finger is simply collapsing because it's weak or habituated to do that, you might try a few left-hand pinky-plucks of open strings and see if those encourage a more advantageous position. As with anything, use common sense and listen to your body.