Why is it called Bas Kol versus Ben Kol?
The Tosafos Yom Tov on the last mishna in Y'vamos (16:6) says that the diminishing volume on each register of an echo is tantamount to weakening. The reverberation is thus associated with the fairer sex.
He also distinguishes between the type of bas kol that is simply the echo of a (meanwhile departed) human's voice and the type of bas kol that is some form of prophecy. Since the the mishna is dealing with the former, the explanation of the terminology might also be limited to that type. Whether there would be any reverberation involved in the prophecy-type bas kol is unknown to me. Since that is the basis of the explanation of bas as opposed to ben, this could be significant in fully answering your question according to the Tosafos Yom Tov.
This is the very first question in the Rif. The Rif answers that he never heard anything about it ,but he notes that when lashon zachar is used we can learn from it,but when it's lashon nekeivah we dont.
Rav Shlomo Aviner answers that a daughter is more responsible over what is given to them than a son. He uses the gemara in Bava Basra 141a as a proof(where Rav Chisda states daughters are more prefable). So the messenger of the message should be like a bas.
Rav Chaim Kanevisky writes "since the voice is weak like a woman's ".
From Sefer Shu"t Hashoel 2:434
Text of the Rif:
Meir ben Ezekiel ibn Gabbai writes in Chelek HaAvodah, Sitrei HaTorah 24:
It is called daughter because it was the very end of prophecy, and thus extremely weak on the spectrum of prophecy. Therefore, it is likened to the daughter [who is weaker than the son],the term daughter thus refers the fact that it is a weak form of prophecy; a mere spark.