I believe that the best answer for this question would be B, "her own." She and Death stop at a burial ground for her, which is marked with a headstone. This entire poem is about her dealing with Death after passing away. She views the world from a distant perspective and eventually life from a distant perspective. Hope this helps.
What help do you need since there is no material for me to try and answer here?
I would say that the answer is A. It seems like the best choice.
Why I descend into this bed of death,
Is partly to behold my lady's face;
But chiefly to take thence from her dead finger
A precious ring, a ring that I must use
In dear employment: therefore hence, be gone:
Romeo says that he must go grieve for Juliet and wants to take "a precious ring" or her wedding ring from her finger.
Some people have said that, although Juliet does give Romeo a ring by way of the nurse inviting Romeo to Juliet's bed, Romeo and Juliet did not exchange rings and so Juliet does not have a ring of Romeo's and he has no "dear employment" for it.
He makes this up to get rid of Balthazar.