There is a custom that the bride’s hair is only covered after yichud. This hints that it is sexual activity that creates the requirement, rather than kiddushin or marriage. What about a woman who has never married but who is also not a virgin? While this is rare in traditional society (a girl taken captive, a pogrom, chas v’shalom), it is no longer rare in secular society.

Shalom, Thank you for your question. In fact your question is discussed at length by the rabbis. The Shulchan Aruch (Even HaEzer, 21,2) writes that "Jewish women should not walk bareheaded in the market place, whether unmarried or married". The commentators (ibid) all work hard to define what the law is that forbids unmarried women going about with uncovered hair. (See the Pitchay Tshuva note 2 ibid). And, in fact one opinion does explain that it is referring to unmarried women who have had relations, such as divorcees, widowers, or even those who suffered rape, or had premarital relations etc. While this is one explication of the text, the halacha follows the majority of commentators who explain that single women who have never been married do not cover their hair, even if they have already had relations with a man. They explain that the Shulchan Aruch is referring to unmarried divorcees or widowers only. Alternatively they explain the text not be talking about being bareheaded, but rather translate it to mean forbidding having loose flowing hair, which they apply even unmarried women, (though many dispute this understanding also). The practiced halacha is then for all women who have never been married to remain bareheaded until their weddings. Because this is the practiced halacha, it would seem that if a women was to cover her hair before marriage based on the opinions that obligate a single woman after relations with a man to cover her hair, it would be terribly immodest, and therefore forbidden. Blessings.