You sound like a kind and considerate person! I agree that you should just have a gentle talk with her. There’s a smell in our room, I’ve been trying to figure it out and I’ve checked all my drawers and laundry. I know that neither of us would want to be embarrassed if we had someone over and our room smelled, so could you check your stuff too? Or, I have to talk to you about something. I would never want someone else to say something and embarrass you and as your roommate and your friend I feel like I’m doing the right thing by letting you know that your clothes and our room are starting to smell.
Does she do laundry? I agree that maybe it is possible that she doesn’t know how, or is doing it wrong. I do think that if you use way too much soap, it doesn’t rinse out and dirt and odors stick on. If you get this sense, kindly offer to help or to go down and do it together. You could also try to throw in some tips such as saying “I like to make sure I do my laundry at least once a week so it doesn’t start to smell” Also Tide with Febreze works really well for odors. Good luck!