I’ve had skin cancer, and I usually wear a fedora or cloche with a brim wide enough to shield my face from the sun. Since I have a hat wardrobe, and I wear a hat out of doors during daylight hours, it seemed silly to me to drive to an EF Mass wearing a hat in the car and then changing into a mantilla or scarf once in the church parking lot. A couple of years ago one woman asked me why the hat after Mass. I didn’t dignify it with a response, and subsequently, the priest told me she was wrong for implying that I needed to wear an actual veil or mantilla.
That being said, a baseball cap with a beer logo on it would be decidedly tacky-looking!
In the US, mantillas were usually the domain of elderly women from south and east European extraction. They were popularized by Jackie Kennedy, when the US started going hatless as a rule. Before that, women generally wore hats to Mass, and kept a scarf, a small chapel veil, or a mantilla in their purses in case they decided to duck into church for a visit with the Blessed Sacrament.
What you’ve described with the ribbon-edged tulle is fine. It doesn’t have to be any particular size, and I think it would be an elegant alternative to the poly lace that seems ubiquitous at the EF Masses. You can make it of any color and length you like. I’ve seen some women with such head coverings which match the color of their coats, their hair, or give high contrast to both You might want to cut out a pattern of newsprint, put that on your hair, and fiddle around with it until you get a shape and dimension you like, if you’re so inclined. If you have access to a serger, a merrowed or serged edge would look elegantly simple as well.
Hope you spiritually enjoy your experience!