This is the kind of biblical passage that tends to make modern readers uncomfortable—not just for its supernaturalism, but for its sexism (no similar ordeal is prescribed for adulterous men) and for its harshness. However, if there is one thing I’ve learned over the last three-plus years of reading Daf Yomi, it is that if something in the Bible troubles us, it usually troubled the rabbis as well. The rabbis were very pious men, but they were also practical-minded, and they could not have been happy with a legal procedure that rested on something as illogical and unreliable as magic. Nor did they like the idea of men forcing their wives to undergo a public and humiliating ordeal that might end in their bursting like an overfilled balloon. From the very beginning of Tractate Sota, then, we see the rabbis doing what they often do when confronted with a difficult biblical law: They hedge it around with restrictions and conditions, so as to make it virtually impossible to enforce.Matters actually were more complicated than this. There survives among the Cairo Geniza manuscripts a magical incantation in Hebrew (JTSL ENA 3635.17 and T.-S. K 1.56), copied somewhere in the Middle East in the 11th-12th centuries C.E., which adapts the sotah rite for use without the Temple. How and even whether it was actually used is unknown, but someone seems to have thought that they could revive the practice. For more see Peter Schäfer, "Jewish Liturgy and Magic," in Geschichte—Tradition—Reflexion (Hengel Festschrift), vol. 1, Judentum (ed. Hubert Cancik, Hermann Lichtenberger, Peter Schäfer; Tübingen: Mohr Siebeck, 1996), 542-56.
Indeed, one key thing about the sota ritual is that, by the rabbis’ time, it was completely defunct. Like all rituals that had to take place in the Temple, it could not be performed after the destruction of the Second Temple in 70 C.E. ...
Background on Tractate Sotah (Sota) is here and here.
Earlier Daf Yomi columns are noted here and links.