I would say that it's the public self. The speaker takes her position as a faithful Puritan wife very seriously. This means that, in keeping with the social values of the time, she puts her husband first. In practical terms, this involves accepting that the love she receives from her husband is so great that there's nothing she can give in return by way of reward. Only God can do that.

The speaker's private self, expressed so beautifully throughout the poem, is nonetheless subordinate to her position in society, her public role as a wife. Though the speaker is undoubtedly head over heels in love with her husband, it's important to recognize that this love takes place within the confines of a Puritan marriage. And this is by no means a partnership of equals, no matter how much love there is between husband and wife.