Who are "Bnos Melachim"?
Rashi: They are princesses.
Radak (16): All of this is a parable. Bnos Melachim are the nations, who will obey Melech ha'Mashi'ach.
Radak: Notzerim err and say that this Mizmor applies to their savior; Bnos Melachim are those who turned to believe in him. Refer to 45:7:1:4 and the note there.
Malbim (Derech ha'Muskal): The Nefesh ha'Chiyunis was 'born' in a foreign land. Physicality is called kings, for it rules over the body. In Sefer Koheles it is called "Melech Zaken u'Chsil" (4:13). Powers that stem from it are called Bnos Melachim.
What is the meaning of "Bikrosecha"?
Rashi: They will visit you. This is like "v'Saroseihem Menikosayich" (Yeshayah 49:23). It is an expression of Bikur.
Rashi citing Menachem: It is an expression of Yoker (honor).
What is "Shegal"?
Rashi: It is the queen, like "veha'Shegal Yosheves Etzlo" (Nechemyah 2:6). Radak - the queen, from Yisrael, is called Shegal, for she is special for relations consistently; she is always in the bedroom. The princesses come only when each is called, in her time. Shegal is like "v'Ish Acher Yishgalenah" (Devarim 28:30).
Radak (16): It is Yisrael, the esteemed of all the nations.
Why does it say "li'Yminecha"?
Radak: Even though princesses are among your wives, the queen is on your right.
Malbim: Royal etiquette is that the woman proper for him based on his level is on his right at the time of Kidushin; a woman not proper for his level is on his left.
Malbim (Derech ha'Muskal): Now it describes how this exalted Chasan (the intellectual Nefesh) leaves his palace to betroth Bas Melech Tzor (the Nefesh) for a wife who will obey him. She will be to his right, to help him, and not oppose him. 'If a man merits, his wife is Ezer; if not, she is k'Negedo' (Yevamos 63a).
What is "b'Chesem Ofir"?
Rashi: It is with a collection of ornaments of gold from Ofir.
Malbim: This is a metaphor. Just like Kesem Ofir is dearer than gold, so the Shegal (queen) exceeds [the princesses] in beauty and glory.
Malbim (Derech ha'Muskal): This is a metaphor for good Midos and straight natures.
QUESTIONS ON RASHI
Rashi writes that "Bikrosecha" is an expression of Yoker. What honor is via the princesses?
Radak: Among your esteemed wives will be kings' daughters. Every king of Goyim will glorify himself via giving his daughter to you.
Malbim: They will come to the wedding, for his honor.