M’ikor hadin, only a b’ula needs to cover her hair, married or unmarried; but there are some poskim who will matir an almana and maybe even a g’rusha, if it will help her to remarry.
Also, while it is noble for a married woman to have her hair covered at all times, there are poskim who hold that m’ikor hadin a married woman can have her hair uncovered in her own home and if unrelated men happen to be in her home while her hair is uncovered, so be it. This practice used to be more prevalent in the times of yesteryear’s g’dolim.