In the other bed, the best, our guests dozed on,dribbling their prose. […] (11-12)
Anne says here that she and Shakespeare allowed their house guests to sleep in the best bed. So the guests may have the better bed, but what happens in the bed is a different story. While she and her husband have poetry, romance, and drama, the guests have boring ol' prose. We think she's suggesting that she and Shakespeare had a pretty good sex life.
[…] My living laughing love -I hold him in the casket of my widow's headas he held me upon that next best bed. (12-14)
Even though Shakespeare is dead, Anne imagines that he's still alive. She holds him in his memory, just like he used to lovingly hold her in bed. Sweet and sad, isn't it?