Preheat oven to 450ºF. Line a baking dish with parchment paper and lightly spray with olive oil.
In a saute pan over medium heat, cook the bacon for about 3 minutes on each side, or until golden brown. Transfer to a paper-towel lined plate, let cool then chop.
Meantime, separate the eggs, putting the egg whites yolks into a large glass or nonreactive bowl, and the yolks in another bowl. Whip the egg whites with a hand mixer on high for about 4 minutes or till thick white peaks form when the beaters are lifted out of the whites. Gently fold in the chopped cooked bacon and chives.
Place two even egg white mountains on the lined baking dish. Create a well for the egg yolk with your index finger then place it into the oven for 4 minutes.
Remove the egg whites from the oven and add the egg yolks in the spaces created, before placing in the oven for an additional 3 minutes.
Spread one side of each bagel with half the cream cheese and arugula. On the other side, spread half the mashed avocado. Carefully place the egg clouds on top of each bagel and serve!