The speaker looks at a rosebush and sees something close to a person: good company, and a regal one. The "fine-dressed hip" most likely refers to rose hips, the round fruit that forms after the flowers fade, packed tightly along the branches. Pressed "hip to fine-dressed hip," they look like a crowd of well-dressed courtiers standing shoulder to shoulder, or hips pressed together in a queenly procession.
Then the poem turns. This queen has "the strictness of the poor / who cannot buy a crown." Her elegance isn't extravagance. It's discipline, the careful, spare dignity of people who make do with what they have. The bush wears no crown, yet it carries itself as though it deserves one.
The mood is warm, quietly admiring, and a little wry. The speaker seems to find companionship in the plain, thorny plant, and respect for a kind of grandeur that has nothing to do with money.