The double-tap-for-iPod behaviour, if people are using the defaults (most people do) only works to bring up the mini player if music is already playing.
Check out Settings > General > Home. As you can see, there are a variety of things the user can choose to happen on double-click. Below that list of things, there is the option for "iPod controls" - when playing music, show iPod controls. This is what you want, and unfortunately there is no way you can choose to override the default behaviour and show iPod controls when music isn't playing.
There are 2 other options (both for the user, not you unfortunately):
- If they turn the screen off, whilst in your app, and then double-click the home button, the mini player will show on screen and then they can play music. They will then still be within your app when they turn on and unlock the screen.
- If they have a 3G-S or latest iPod Touch, then holding the home button will bring up the voice command menu, from which they can play music. They will then still be in your app when that menu closes.
Probably not the answer you wanted, but that's iPhone development for you!