With apologies if I may intrude with a male view on the topic. Many of us male type critters use a purpose designed gym bag, mine is labeled OGIO. These are stand up bags with a full opening front, internal shelf, pockets on the "door" for various items and an external zipper pocket on the door. They are not "cute" but are functional having a shoulder strap as well as handles. Other bags have a separate opening for shoes or a lower compartment for shoes. My partner uses ziplock bags to carry her necessaries when going to the gym or traveling.
The OGIO ones can be a bit dear but you can often find them at thrift stores. Here is a similar one from Walmart. www.walmart.com/ip/Goodhope-Bags-18-Small-
Just a couple of suggestions.