Women Hair Covering: Divorced/Widowed
Question
Is a woman who has been widowed of a non-Jewish husband required to cover her hair? Also: if she has not covered her hair since being a teenager, should she cover her hair when studying Torah and going to Shul?
Answer
A divorced or widowed woman is required to continue covering her hair, as it says, “Jewish women do not go out in public with uncovered hair regardless of whether they are married or single.” The term “single” does not refer to teenage girls or women who were never married but, rather, it refers to women who were once married and are now single.
While all authorities agree that the obligation for married women to cover their hair is a Torah obligation, some rule that the obligation for “single” women to cover their hair is a rabbinic one. Others rule that it is a Torah obligation for both divorced and widowed women to cover their hair.
However, in your case you don't need to cover your hair since you are not considered as married by Jewish law.
Source
Sources: Rambam, Hilchot Issurei Biah 21:17; EH 21:2; Beit Shmuel 21:5; Chelkat Mechokek 21:2; Aruch Hashulchan, EH 21:4;