Rosemary plants grow well here in Arizona.
Where is it coming from?
To answer that question, check out the structure of the rosemary flower up close. See those "antlers" sticking out of the top of the flower? The ones with the deep purple pads on the ends are the stamens. The purple pads are the anthers, where the pollen is released.
When the honey bee sticks her tongue deep into the throat of the rosemary flower to suck up the nectar at it's base, the stamen catches her on the back of her head and thorax. Like a pad full of powder, the anther dusts her with pollen.
Note: the photographs are a bit blurry because the honey bees were visiting each flower for only seconds at time.
Have you ever seen a flower dust pollen onto a honey bee?