Because Beatrice herself sent him. In canto XXXI Dante turns to ask her the things he had left hanging and sees, in her place, an old man with a kindly look, as befits a tender father. He cries out, "where is she?" and the old man replies that Beatrice moved him from his place to bring Dante's desire to an end, and that Dante will see her again in the third circle counting from the highest rank, on the throne her merits have earned her.
The exchange marks the passage from one method to the other. Beatrice argues, Bernard prays. Throughout the canticle she has explained the order of the world, the vow, justice, and the choirs of angels; now what remains for Dante is not won by explanation, and Bernard says so in canto XXXII: whoever believes he is advancing by beating his own wings may be moving backward, and it is fitting to ask Mary for grace. That is why his last lesson is a prayer.
As for why Bernard, and not another saint, the poem answers only with her will, and for many readers that answer does not settle the matter. Dante prays to Beatrice, she smiles and returns to the fountain, and what she began is fulfilled in the request the saint makes to the Virgin. Her farewell no longer uses words.