How come the glue thats in the bottle doesn't dry up?

Because of it's moisture

the answer is simple ... air. There is no air in the bottle so glue does not dry but when the glue reaches or comes into contact with air then the glue drys up and become dry. The same goes with the glue sticks also. Once the glue stick is opened and you put the glue from the stick on the paper or whatever it is your gluing the air will hit it and it will dry. 

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it's all together and it will dry if it's sitting forever

Because it is sealed from air. That prevents drying out.

The cap keeps the moisture from evaporating out of the bottle. When it's open, it will still take a long time to dry as it dries from the outside in. That's why it takes a lot longer for a big clump of glue to dry than a thin spread.

My glue bottle doesn't have cap? .

Most glues work by the solvent evaporating from the dab of glue. The bigger the area exposed, the faster the solvent evaporates. In the bottle, the area is minimized. It does dry up if left long enough, especially at the top surface, but very slowly.

It does if you leave the cap off.

The cap keeps the air out.