There is a preload option in jPlayer:
The jPlayer constructor option jPlayer({preload}) is used to control
when jPlayer begins downloading new media. Some browsers will begin
the download for the whole media when the preload option is "metadata".
Others will require that "auto" is used. The only way to ensure
download does not begin automatically is to use the preload option "none".
Remember that, the media may not download as it depends on the browser
you are using. Mobile browser such as Mobile Safari on iOS 4.2 require
a gesture before any media is downloaded or played. ie., The user must
press a button to initiate the load or play operations the 1st time.
Alternatively you can leave the player without mp3 for initial page load and only add it when the user clicks play. See this demo for an example of loading media to the player: http://jplayer.org/latest/demo-02-jPlayerPlaylist/