Exode 2:5

And the Word of the Lord sent forth a burning sore and inflammation of the flesh upon the land of Mizraim; and the daughter of Pharoh came down to refresh herself at the river. And her handmaids, walking upon the bank of the river, saw the ark among the reeds, and put forth the arm and took it, and were immediately healed of the burning and inflammation.

TO BATHE ‘AL’ (BY) THE RIVER. “Transpose [the order of the words in] the verse. Rashi explains it to mean: “And the daughter of Pharaoh went down by the river to bathe in it.” and then explain it: the daughter of Pharaoh went down by the river to bathe in it.” Thus the language of Rabbeinu Shlomo [Rashi]. If so, al haye’or (by or upon the river) is like el haye’or (to the river). Similarly, And Elkanah went to Ramah ‘al beitho’ (upon his house) [is like el beitho (to his house)]; Thus shall ye say every one ‘al rei’eihu’ (upon his neighbor) and every one to his brother [is like el rei’eihu (to his neighbor)].
It is possible that there were steps upon the bank of the river and that she went down from the royal palace to bathe upon the first step by the river, but did not enter into the river’s stream. [In this case, the expression al haye’or would be completely understandable, as it would mean that she came down to bathe “upon the step near the river”], and then she saw the ark among the reeds far from her and she sent her handmaid to fetch it. It may be that to bathe ‘al haye’or’ is like “to bathe baye’or (in the river).” Similarly, And thou shalt put them ‘al’ one basket [is like b’sal echad (‘into’ one basket)].

אמתה, not “her nursemaid,” but “her maidservant.”

לרחוץ על היאור. She had a view of the river, her room in the palace bordering on the embankment. No doubt, royal etiquette would not permit an Egyptian princess to actually bathe in the river. [the author was alerted by the preposition על instead of ב, “in,” in front of the word יאור. Ed.]

ונערותיה הולכות, this is the reason why she did not command one of them to bring the basket to her as they were not with her at that time.

ותשלח את אמתה, the servant who was attending her at the time when she bathed herself. All of this happened at the instigation of G’d so that she would not dispatch one of her regular attendants as she might mistakenly place her trust in them and such an attendant would throw the baby in the river.

ותשלח את אמתה, “she sent her handmaid (to fetch it).” In the Talmud, tractate Sotah folio 12, two sages disagree concerning the meaning of the word אמתה here, one claiming that it refers to her forearm, (The princess’;) According to one sage this was a bodily owned slave, שפחה, whereas the other sage the princess went down to bathe on her own. [The author speculates how to reconcile the opinion of the sage who claimed that she sent forth a slave with the aggadic statement that an angel struck down all but one of her slaves at the time. [This editor does not follow the need for these far fetched interpretations, and I have not pursued them further. Ed.]