Medieval bras at the University of Innsbruck. The university press release has more details than the AP report. They found a lot of other stuff besides.
Romans had halters for sports, so this doesn’t exactly shock me. In fact, my dark suspicions are confirmed. Fitting this kind of bra would not be a fun sewing job, however, so probably not in use among women who weren’t rich or crazy-good seamstresses.
However, the article mentions that “shirts with bags” do come up in written evidence. Making a circular drawstring bag or pouch of a certain size was not a difficult project; beginners can make them today. So if women just took a shirt, cut holes in it, and sewed bags of reinforced fabric into the holes in a supportive way, that would be something that would be trickier in the measuring than the making. You could even try on the bags before sewing them to the shirt. You could then wear your real blouse, shift, etc. on top of your “shirt with bags.” If you constructed the shirt in parts around the bags, you could get a pretty good fit. It would be picky, but not impossible. Lacing up the sides or other bits would also allow a more adjustable piece of clothing.
The “tuttenseck” (I love that word!) is an even simpler concept.
UPDATE: The archeologist Beatrix Nutz who discovered this stuff (yeah, it’s a great name, isn’t it?) has a more extensive article in BBC History Magazine.