The Bakh, Part 1: His Text

לא ילכו בנות ישראל פרועות ראש בשוק אחת פנויה ואחת אשת איש: נראה דנפקא לן מדאיתא פרק המדיר (כתובות עב.) ואיזהו דת יהודית?  יוצאה וראשה פרוע.  דאורייתא  היא דכתיב (במדבר ה יח) "ופרע [את] ראש האשה"!  ותנא דבי רבי ישמעאל אזהרה לבנות ישראל שלא יצאו בפרוע ראש.

 דמדלא קאמר אזהרה לאשת איש אלא סתמא אזהרה לבנות ישראל אלמא דאחת פנויה ואחת אשת איש באזהרה.  מיהו במרדכי כתב ס"פ [סוף פרק] מי שמתו (ברכות סי' פ) ע"ש  "[וכתב] ראבי"ה (סימן עו) וז"ל [וזה לשונו]: "כל הדברים שהאזהרה למעלה לערוה דוקא בדבר שאין רגילות להיגלות אבל בתולה הרגילה בגילוי שער לא חיישינן, דליכא הרהור" עכ"ל [עד כאן לשונו].

ואין לפרש דדוקא בבית ובחצר אבל בשוק אסורה לצאת  דהא ברפ"ב [ראש פרק 2] דכתובות (טו: ) שנינו אם יש עדים שיצאת בהינומא וראשה פרוע כתובתה מאתים ויצאת פירש"י [פירש רש"י] (ד"ה [דיבור המתחיל] אם יש עדים) מבית אביה לבית בעלה ואפי' [ואפילו] דרך השוק 

משמע, וכן נהגו וצריך לומר דבפנויה בעולה קאמר, אבל הבתולות אינן באזהרה. 

The daughters of Israel do not go with an uncovered head in the marketplace,  both an unmarried and a married woman: It seems to originate in what it says in Ketubot chapter “” (daf 72a): “What is Dat Yehudit?  She goes out with an uncovered head.  But that is from the Torah, as it says (Numbers 5:18) ‘And he uncovers the head of the woman’ [context is the Sotah ritual, as explored in these posts].  The house of Rabbi Ishmael says, a warning to the daughters of Israel that they should not go out with an uncovered head.”

Since it does not say “a warning to a married woman”, but rather simply “a warning to the daughters of Israel”, both unmarried and married women are included in the warning.  However, in the Mordechai, at the end of Brachot, chapter “One Whose Dead”, section 80, it says “the Ra’avya writes: ‘All the matters in the warning about is specifically about erva [nakedness], in a matter that they do not usually reveal, but we are not concerned about a virgin, who is accustomed to revealing her hair, because there is no [concern over] improper fantasy.”

And one should not explain that this [that a virgin goes with an uncovered head] is specifically in the house or courtyard, but [her going with an uncovered head] is still forbidden in the marketplace, because at the beginning of the second chapter of Ketubot (15b) it says that if there are witnesses that a woman went out in a hinuma, and her head is uncovered, her ketubah is 200.  [Going out in only a hinuma is sufficient legal evidence that she was a virgin when she married, and therefore gets the higher ketubah value.  This implies that unmarried virgins do not cover their hair, even in public.  For some more about the ambiguous meaning of the term hinuma, see this post]  Also, Rashi explains (in his comment beginning: If there are witnesses) that this means when she goes from her father’s house to her husband’s house, even by way of the marketplace.  This is our custom, and therefore it is necessary to say that the Tur meant a non-virgin unmarried woman [when he said that unmarried women also cover their heads], but virgins are not included in the warning [from the house of Rabbi Ishmael, in Ketubot 72a.]  

This seems pretty lengthy already- so some thoughts about the Ba"kh's position (and the usual information about who he was) will come in a following post.  I will add here that the quotation from the Mordechai comes from his comments on the recitation of the bedtime Shema.  This is a digression based on the principle that he is establishing for what a man may see of his wife while reciting Shema.  In my mind, that almost makes it more reliable, because it isn't on the topic where he might have something to prove, at that point, it's just a good sociological proof, from his perspective.