The bladder that you mentionned, is actually a damper, to prevent the variations of the pump from being felt at the faucet. Without it, the water would pulse out. It also acts to steady the pressure. It doesn't actually pump any water.
Now if you want to use a bladder to pump water, then what you're talking about is essentially a bilge pump, and most of us will tell you that it's not a good idea, because they break fast: they're not meant to run for a long time.
If you're looking to increase the pressure, you'd have to keep in mind that it's a closed loop, so the pressure has to be lost somewhere, making it an open loop. The pump isn't going to like it, I can tell you that right now!
Keep at it, there might still be something in the idea.
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