In this poem, the "She" of the title and first line seems to apply to the bee, and this poem presents us with an evocation of the bee's work and beauty. The bee, according to the first stanza, is above all hardworking and incredibly industrious, as the bee is the first creature to rise and begin working, and the last creature to hide itself away at night when darkness falls. So short, in fact is its period of rest that:
Her Night doth hardly recompense
The Closing of Her eyes--
The reference to purple that your question refers to comes in the second stanza, which uses the colour purple in a very interesting manner. Normally, in other Dickinson poems, the colour purple is associated with importance and majesty, such as when Christ's robes are described as being purple. Note how it is used here:
She doth her Purple Work--
In what ways can the bee's work be described as "Purple"? Perhaps Dickinson is saying that the bee's work is "Purple" because it is so important in helping nature grow and produce, which bestows upon the bee a position of great importance and magnitude. What is clear, however, is the way in which the bee's example is one for us to follow, as the last stanza makes clear.