The clearest picture we get of love in "Bright Star" comes after line 9, when the speaker describes how he wishes he could spend all eternity with his head resting on his "fair love's ripening breast." In fact, he desires this so much that he wishes he could "swoon to death" if it can't become reality. In the beginning of the poem, however, things are more ambiguous. Depending on how you interpret the description of the star and the moving waters, they could be motivated by love too, or, if "love" is too strong a word, then devotion, or care. What they are devoted to or care for is a trickier question – whatever it is, they don't seem to be too interested in humanity. At the end of the day, the most important aspect of love for the speaker in the poem is the deep connection it creates between human beings. In this way, love stands in contrast to the cold isolation of the rest of the universe of the poem.
The speaker of the poem focuses on his girlfriend's body because this is what connects her to mortality.
Even though the poem talks a lot about love, it is really more about death and human existence.