The bonus bar increases each time you receive a duplicate cover. When the bar is full, your next cover is guaranteed to be new. The bar resets each time you get a new cover.
The October 29, 2013 Patch Notes state:
We are introducing a new progress bar which should allow users to see how close they are to receiving their next guaranteed NEW collection cover. The math for new covers has not changed since we originally launched the feature. We are now just visually showing what’s always been working in the background, and it works as described below:
You have a chance to receive duplicate covers until you have received a number of duplicates equal to the number of unique covers you currently own IN THAT COLLECTION. Each collection has its own counter and does not influence the chances of duplicates in other collections. Here’s an example below.
You open your 6th NEW cover and now have 6 unique covers in your collection unlocked. You only need 2 more covers to unlock Loki. You now have a chance to receive up to 6 duplicate covers before you receive your 7th NEW cover for your collection. However, each duplicate you receive REDUCES the chance you will get a duplicate on your next lockbox opening.
The progress bar we’ve added to each collection page will show you how your chances to get a NEW cover are increasing as you get duplicates and hopefully will make it easier to determine how close you are to obtaining the lockbox hero.
Of course the example above applies to both opening 1 lockbox and 10 lockboxes at a time, but the chance to open any cover at all when opening 1 lockbox never changes. So be aware that in most cases opening 10 lockboxes at a time will complete your collection faster. Unless you’re lucky!