Again, since the wikiloops community does not benefit from your private jamming fun, the option to form private band projects is available to "supporting members" only!
If you want to share your music with selected wikiloops-members only - be it your real life band companions or a group of users you invited from the community - starting a band is the way to go.
Since there is not much sense in starting a band without any song material, the place to start a band was added to the session-template upload dialogue, which is available to registered users on the jam-view pages.
If you hit the option 'private session' there, you will be asked to form a band in the next step (or you'll be able to select a band you've started or been invited to earlier).
You may start as many bands as you like.