As so often with Shakespeare, the problem you're having here is, I think, because you've plucked a single phrase out of context. Here's the whole passage:
O, speak again, bright angel! for thou art
As glorious to this night, being o'er my head,
As is a winged messenger of heaven
Unto the white-upturned wond'ring eyes
Of mortals that fall back to gaze on him
When he bestrides the lazy-pacing clouds
And sails upon the bosom of the air.
It's Romeo in the famous balcony scene (2, 2). He implores Juliet to speak again - though she can't hear him. It's difficult to paraphrase, as it's all one long sentence. But.. Romeo says that Juliet is "as glorious to this night" as a messenger, with wings ("winged") from heaven would be, if he appeared to mortal men's white and upturned (so they can see the heavenly messenger in the sky) eyes. The mortals eyes' have to fall backward (literally) to be able to look up to see the heavenly messenger, because he "bestrides" (sits astride) the slow clouds, and soars ("sails") upon the air's bosom.
"Bosom" here just means breast, so Romeo does indeed personify the air as having a breast which the heavenly messenger can "sail" astride.
In summary - Juliet is as glorious to Romeo as a heavenly messenger would be to humans, if he sailed on the air.
Hope it helps!