That would depend on several factors - first, how much do you care about historical accuracy? second, what is your social class? third, would your character wear hair-coverings with an English, French, Italian, or Spanish ancestry? fourth, how much do you want to do for yourself, beyond fitting a piece of mesh? fifth, and this is strictly hypothetical, how do you feel about Henry's proposal to have his marriage to Catherine (Spanish Caterina) annulled, so that he can try for heirs to connect England to stylish France?
Historically, women wore hair-coverings at this time. Lice were rampant, and preventing socially transmitted diseases was about prophylactic devices of all kinds. If you could afford to wash and have neat hair, it had become fashionable to drape the hair-covering back from the face and let the hairline show.
For instance, here's a picture of Catherine of Aragon, from the awesome website, Grand Ladies. It looks like Catherine sat for it at about the time of the death of her first husband, Arthur, Henry's brother.
The album of portraits from 1500-1559 on the Great Ladies website is a good collection for the study of fashion for this time.
Catherine would become famous for promoting the pious "Gable Hood," which is said to mimic the structure of a church roof. So the English seem to be taking things square and straight.
The French meanwhile are rounding the edges of the head-covering to create soft shapes around the face. The heart-shaped "Atifet" hood had appeared by around 1550. Descended from the "French Hood," it became famous later as worn by Mary, Queen of Scots. (For a good general reference on the French Hood, see the FashionHistory Wikia page.)
The Italians had never really caught on to the "Hennin," that cone-shaped hat that most of us remember when we think about medieval ladies. The Gable seems descended from the Hennin, so Italian head-coverings went a different direction, Their head-coverings seemed to have less structure; most women in portraits I've seen tend to wear snoods or even lighter hair nets, which may have become a marker of social class, usable only when your social circle--including the servants--is completely free of head bugs. Anabella Wake has a nice page on 1520s Italian fashion on her larger Italian Renaissance historical fashion site, Realm of Venus.
Lady Jane Seymour was wearing a Gable hood again by the time of this portrait, around 1536-1537.
Lady Jane Seymour, c.1536 |