The Kessef Mishneh (Hilkhot K'riat Sh'ma 3:3) quotes Rabbenu Manoah who cites an opinion that the reason not to make blessings in a bath house is because of the presence of naked people. Accordingly, in a ladies' mikveh, one should similarly not make a blessing. However, Rabbenu Manoah himself states that the reason not to make blessings is that the water is dirty given the usage of hot water, but in a mikveh that uses cold water there would be no problem.
Accordingly, R. Ovadya Yosef rules in Taharat HaBayit (Vol. II: 15:1) that the blessing should not be recited in modern day mikvaot, since the water is warm.
However, Rabbenu Manoah doesn't elaborate why exactly a mikveh would get so dirty form using hot water (perhaps they effectively cleanse the women of dirt?), and modern day mikvaot stay quite clean, in spite of hot water, so it seems likely that according to Rabbenu Manoah, it would be permissible to make a blessing in a mikveh.
Furthermore, R. Qafih (notes to Hilkhot K'riat Sh'ma there: 13) notes that Berakhot (3:5) discusses reciting sh'ma in a mikveh. He explains that immersion in a mikveh is brief, unlike a bathhouse in which naked people congregate.
Additionally, see Birkat Moshe by R. Aviad ben Shalom Ashual (11:9: pg. 366).