Q:

Feasibility of a Synthetic Buoyancy Bladder, Used in the Air

Many fish have specialized organs called buoyancy bladders which allow them to control their buoyancy - effectively rising or sinking in the water.
What if humans adapted this to use in the air? I'm picturing something like a balloon, strapped to the user's back, that filters specific gasses less dense or more dense than air to fill itself. It would be able to calculate what ratio of x to y was necessary to move the person up, down, etc.
A) Is there any reason this is not possible, and
B) If possible, what are the limitations / things to consider?

A:

The issue is how are you going to inflate it.
A fish has it easy, it can just take some of the gasses dissolved in the water and pump them into its bladder with enough pressure to stand the exterior pressure. Since gasses are way lighter than water, it does not need a very large bladder.
Now, you have your humbird (human bird) with his bladder. The first issue is that it must be HUGE. Since air only weights slightly over a kilogram per cubic meter, the most buoyancy you get will be that 1.225kg per cubic meter (at sea level, less as you rise), and that assumes that the bladder is void.
But let's forget about that and guess that you are happy with that "humzeppelin" design. Then appears the issue of how to fill that gigantic space.

If you leave it void you need a very strong structure to avoid it being crushed by atmospheric pressure (ever tried the experiment of making the void in a can?). Strong structures are heavy.
You may fill it with something to avoid or limit the pressure differential. But.. what? The gas that you have freely available is the same that the one you have to float on, so it is not going to provide much lift. Heating that gas might help, but then again you will need important amounts of fuel to heat such a gas, and it is not like you can ignite fires in the interior of living beings.

You may try to justify that your animal has some internal deposits of, say, compressed helium inside (again, compressing helium is not small feat for a living being), but the issue is again where will you get your helium from (free helium is light, so it goes to the upper atmosphere and goes into space; our supply of helium comes as byproducts of nuclear decay that got trapped in oil deposits).
Another option would be the animal producing hydrogen by some chemical reaction, that is feasible but is a great risk for the animal (not only because what happened to the "Hindenburg" but also because hydrogen is highly reactive with organic tissues).

A:

Getting lift is the only problem. People are innately able to get to the ground from any height without external assistance. The ratios are well known.
A) It's possible, but not even close to feasible to "filter specific gasses" like hydrogen or helium from the atmosphere at ground level in order to lift a human (about 68 cubic meters for helium). It's more feasible to generate, from water via electrolysis, enough hydrogen to a lift a human (about 58 cubic meters).
B) One things to consider is that the difference between a human's density and their surrounding medium is significantly different than the difference between a fish's density and its surrounding medium. This means a fish can make rather subtle adjustments to change its vertical position, but a human needs to inflate a balloon the size of a shipping container. Additionally, while fish can swim at any height in the water, humans can't walk once they're four inches off the ground. Floating humans will just blow in the wind.
This idea was explored in Neal Stephenson's book Anathem. Humans in this book had spheres which increased their volume without allowing air or any other gasses to enter them. That is, they filled with vacuum. Which is an even better "lifting gas" than helium or hydrogen (marginally). If you're not restricted to hard science, I suggest you explore the vacuum lifting spheres, then there is no need to mess with filtering rare gasses out of the atmosphere.

