Me, Myself, and I
Dickinson has a lot of quirky writing habits, but one that stands out in this case is the first person speaker. Sometimes Dickinson will use "I" to indicate the speaker and "you" to indicate the reader, which sets up an interesting relationship between the reader and the poem. Being addressed directly like that makes the poem feel very real because we've been invited to be a part of it. This poem, however, just uses the "I" because, even though we are privy to the inebriation, this is more or less a private moment for the speaker. She is so wrapped up in the ecstasy of the moment that she doesn't notice, or even care, that others may be watching. This makes the poem seem more pure and genuine. It illustrates the essence of that whole "dance like no one is watching" thing—it doesn't matter what anyone thinks, she's going to revel in her drunkenness whether you watch (or approve) or not. For more examples of this, check out "I like to see it lap the Miles" or "It's all I have to bring today".