Why does the King James Version use word "bottles " in Luke 5:37-38 and not "wineskins"?
The word used in the Greek original is ἀσκός “skin, hide”, but usually a “skin made into a bag, wine skin”.
The point of the Biblical parable is that a wine skin will dry out with age and become brittle. If you put fresh grape juice in an old wine skin the fermenting of the wine will cause the skin to burst. That is why you need to use a new skin.
But your question is basically a question about English usage. The Oxford English Dictionary defines "bottle" as;
"A container with a narrow neck and wider body, for holding or storing liquids, pills, etc., now usually made of glass or plastic, but formerly typically of leather, wood, earthenware, or metal."
and has numerous examples for the use of "bottle" for a leather wine-skin, e.g.:
a1529 J. Skelton Colyn Cloute (?1545) sig. B.viiiv, They were wonte to drynke Of a lether botell.
"Bottle" is used in English translations of Matt. 9:17 (=Mark 2:22 and Luke 5:37-39) beginning with the Old English "West Saxon Gospels":
Ne hig ne doð niwe win on ealde bytta
And similarly in all the English translations of the Bible, down to the KJV and beyond.
The phrase "new wine in old bottles" has remained a common expression in English.