She should pay rent- just an investor's perspective. ;)
In all seriousness, it might sound a little "cold" to ask her to pay rent straight up, but I don't really think anyone (man or woman) should have a free ride. I think you should frame it in a way that explains the ongoing cost of property ownership (including whatever % you will be setting aside each year for capex), and that, without her, you would be collecting rent from a roommate to help cover those expenses. Come up with whatever her share of the expenses would be. If you really want to feel ok about it, you can compare that number with what you would have charged a roommate. The difference between those two numbers would be the "profit" you are leaving on the table (assuming you could get more from a roommate). My logic here may be a little convoluted considering the property is a duplex and you're house hacking but this is what I would do in your shoes.
(It's worth noting that you'll need to have her sign some kind of rental agreement for legal purposes.)