I was thinking that the area where the bullet is pushed onto the casing could be made air-tight, and the percentage of oxygen in that area increased. This would cause a higher percentage of oxygen to be inside of the closed bullet. This should make the bullet more powerful with the same amount of powder. For pistols it could guarantee that all of the powder is burned before the bullet left the barrel, increasing the power of the bullet.
The percentage of oxygen in that area could be increased in increments and the bullets tested to see if they are stable and would not go off when you don't want them to. The temperature at which they would go off could be tested also. Also the muzzle velocity of the bullet and its power would be tested. These tests would be done at each stage of increase in the percentage of oxygen that is used when the bullet is pushed onto the casing.
It seems to me that if pure oxygen is in the bullet, something like card board ( and many other things) would burn fast like gun powder and would be suitable to propel the bullet.

The oxygen content could be increaced even more easily by simply adding more of the oxydizing agent. In the case of gun powder, (Also refered to as black powder), the oxydizer is saltpeter. I don't know if an increace in the oxydizer would improve the standard performance or not.

Modern ammunition uses what is called gun cotten. It is designed to burn a little slower than black powder because of the rifling, (small grooves inside the barrel of the gun which cause the bullet to spin when fired), in modern firearms. This spinning slows the bullet slightly and if black powder is used could cause the breach of the rifle to explode in the shooters face. Hence the use of gun cotten which is slightly less volitile.

In most of the United States it is illegal to pack your own bullets without a license. No matter where you live you should not attempt to pack your own bullets unless you have had extensive training. All explosives are dangerous. You should never attempt to alter or in any way tamper with store bought ammunition.

Other than that, happy shooting, my fellow gun nut!

Agreed. The oxygen comes from chemicals in the gunpowder, not the tiny bit of air trapped in the cartridge. I'm sure people have already figured out the optimum ratios of chemicals that go into gunpowder.

Black powder: usually leaves a large amount of residue, depending on constitution; some recent developments have altered the residue from acidic (sulfuric and nitric) to non-corrosive, such as a combination of potassium nitrate and citric acid (yep, vitamin C). Residue from that is mostly water, I guess. But I did make some up and it did work.
Gun cotton: this is the base for modern smokeless powder; however, gun cotton is actually nitrocellulose, and is extremely unstable, as witnessed by the explosions of the facilities in Germany in the 19th century. This stuff is made stable by soaking it in ether, then balling it up, wadding it up, and then coating it with graphite. There is very little residue from smokeless powder, as the nitrocellulose recombines almost completely into gas (something like 99%, vs 60-70% for black powder).
Lord says oxidants are within the powder, and this is true. Adding air or oxygen wouldn't do much. Using black powder in a modern weapon does nothing, and will ruin your gun, as it will in a muzzleloader if you don't clean it. The simplest way of adding power is to lengthen the barrel to allow more burn time. Also usually will increase accuracy due to spin stabilization being somewhat better.
Been loading for a long time. Never heard of it being illegal. Clue me in on that.

Modern ammo uses cordite or nitro cellulose. It burns much faster than black powder and is smokeless. An added amount of oxygen in the space in a bullet should help the powder to burn faster and cause more of the powder to burn before the bullet leaves the barrel increasing the pressure and bullet velocity. The oxydizer would take longer to produce the oxygen. Oxygen that is already in the bullet is available much faster.

The best way to add oxygen to the mix would be to do it chemically. Simply adding air to the bullet may give it lets say a tenth of an ounce of air, which is not totally oxygen. The chemical reaction that takes place from an oxydizing agent would add more oxygen and also, it would be another expanding gas. I agree that a longer berrel would be a far better way to add power and accuracy at the same time.

Nitro cellulose is also known as Gun Cotten. From what I understand, cordite is used primarily in large guns, like those found on battle ships and in field artillery. I'm sure that someone is marketing cordite charged bullets but, I don't know who or that I ever used them specifically.

It would be wise to find out which state agency oversees hunting in your state and inquire with them as to the specific laws regarding loading your own bullets. They would either be able to tell you or put you in touch with someone who can. I could tell you about Georgia but, if you live only seventy miles away in Alabama, the information would not be useful and could even lead you to a fine. I wouldn't want to do that.