[…] My lover's words were shooting stars which fell to earth as kisses on these lips; […] (3-5)
This is a crazy double metaphor. Shakespeare's words are like shooting stars, and those shooting stars are like kisses on Anne's lips. Shakespeare's words are so powerful that they materialize into real tangible kisses, which Anne can feel. Intense!
[…] my body now a softer rhyme to his, now echo, assonance; his touch a verb dancing in the centre of a noun. (5-7)
Anne describes she and her husband's passion in terms of poetic devices: rhymes, echoes, assonance, verbs, nouns. It's like Shakespeare's writing comes alive.
Some nights, I dreamed he'd written me, the bed a page beneath his writer's hands. Romance and drama played by touch, by scent, by taste. (8-10)
Here, Anne seems to suggest that she's a character in one of Shakespeare's plays. Still, she's pretty lucky. Though other people only get to experience Shakespeare's words by reading his poems or seeing his plays, she gets the full-on sensory experience.
In the other bed, the best, our guests dozed on, dribbling their prose. […] (11-12)
The guests get to sleep in the best bed, but what happens in that bed is
only prose. Over in the second best bed, Anne and Shakespeare have
poetry, romance, drama. It sounds like the second best bed is the place