nrathaus is correct. Bitly doesn't control the data sent from your server. We send a 301 redirect, which your browser should cache, but there is no content in that response other than the location of the long URL.
You should make sure that "www.myzerver.com/myjson.txt" is sending the appropriate headers to tell your browser to never cache it. See this StackOverflow answer for details on which headers to send.