I have been attempting to pair a Vivofit Jr to an iPhone as well. Bluetooth connection is good as is shows the number displayed on the jr to pair, but then pretty much immediately comes up with 'Network Error' 'Failed to pair kid band. Cannot connect to server. Please check your network connection and try again later.' On an Android phone, it connects immediately.
Not sure if this will help, but I was having these issue as well. I went into my Bluetooth settings and enabled "Phone Visibility". I was then able to connect to my jr.