The theme of loyalty is a very important one in "Bright Star," because it is so closely wrapped up with the idea of "stedfastness," the quality that the speaker admires most about the star. It quickly becomes clear, however, that it isn't enough just to have the staying power of loyalty: you also have to be loyal to the right things. It might be pretty impressive and all that the star keeps watching the waters and the snow for all eternity, and that the waters keep washing the shores for all eternity, but that doesn't really interest the speaker of Keats's poem. Instead, he wants to devote his loyalty to the woman he loves – by remaining forever with his head resting on her breast. Of course, things get a little more hazy at the end of the poem, when the speaker says he would rather "swoon to death" if he can't have this desire fulfilled. Is this just a cop-out, and therefore a failure of loyalty, or is it just the ultimate expression of how profound the speaker's loyalty really is?
Being "stedfast" and being loyal aren't the same thing in this poem; you can only show loyalty by being devoted to somebody else.
When the speaker says he would rather "swoon to death" if he can't spend all eternity with his head on his girlfriend's chest, this shows that he is a bit self-serving and not as loyal as he thinks he is.