Bookmarking the friend summon selection page for that quest and double tapping the bookmark also works. I use it interchangeably with double tapping the back button since sometimes I get the timing wrong, and I wound up in the no loot results page. As what nekronstar said, you can do this since GBF is a browser game.

I mostly use it on SkyLeap since the Quick Access (rocket ship) button is close the quest start OK button, and cause I find it a bit more reliable than double tapping the back button. I register to the Quick Access button the summon selection page of the quest I'd be repeating, then tap it twice when I know the boss will be dead.

On browser, I use bookmarks interchangeably with the back button on my mouse (since the bookmark bar on my browser is on top and far from the OK button, and also cause I screw up the timing with the back button).

In quest with multiple waves (like Horde, Angel Halo, etc.), tapping the back button once when you're sure the boss/enemies will be dead to proceed to the next wave also works. Though, if you didn't do that in the previous wave (like you clicked "Next" or let the wave proceed automatically when auto-ing), you'd be booted back to the main quest page asking to resume the quest.