Lack of air, the moisture in air is what makes it stick.

Nothing, except as long as the glue is flowing only a thin layer sticks to the bottle.
Then there are different kinds of glue. The super glue fort instance is hardening under the influence of moisture as Hiheels mentions above. Other types of plastic harden slowly, and then a thicker layer, and eventually all glue, sticks to the inside.
Many types of glue consist of a solid organic in a solvent. As the solvent evaporates the glue gets thicker with he same result.

(I know, this is not the common answer to this common fun question)