Hey there princess!
With Rush 2024 on it's way, I know that a lot of girls are prepping their Rush bags for the week. I went through Rush in Winter 2009, and became a Kappa Alpha Theta at Baylor University. My experience was incredibly positive, and I am aware that things today are different than they were back when I went through Rush.
When I went through Rush we all wore our winter coats (Baylor Rush still takes place in January) and purses aren't allowed in the room. My solution was to keep a lipstick, pocket mirror, ID, and my Motorola Razr in my coat pocket and leave it outside of each room (Baylor also doesn't have houses). Below are some ideas of what I would use as a Rush bag if I were to go though Rush today, and some essentials I would keep in the bag. Please keep in mind that I am not being paid to advertise any of these items, they are just things I really like!

These are just a few examples of some bags that I think would be great for Rush (and for college students in general) because they:
A. All have zippers
B. Are all customizable
In a sea of girls tossing around a bunch of identical bags that they bought on Amazon Prime day all over the place, you want to make sure that your items are secure, and that your bag is easily identifiable.
Now.... as far as things to put in your bag...
There is one item that I think is absolutely essential, and that I will recommend again and again and again, and that is this Chanel lip product (my favorite shade is Sensual Rose). I have worn these liquid lipsticks for YEARS, and I am not kidding when I say that they last ALL DAY. It is a great product, and is pretty much the only thing I will wear on my lips.
l absolutely love this pressed powder. There is a mirror in there as well so you can check your makeup throughout the day. Keep in mind the coverage is light!
Sparkle on!