Have her wear her competition bun or hairstyle for a few practices before her first meet. That way she can practice with what it feels like and you can practice with her you need to fix it to make it tighter if it falls out !
This.
Our gym does a mock meet. With judges and full meet dress. 2 reasons. Kids have a baseline of their scores and know what they need to work on based on judges feedback (which helps because validation for the coaches corrections). And so they are used to what they are supposed to do and how their leos fit and feel, How to get warm ups on and off quickly Get used to their hair etc.
If your gym doesn't do this. Practice at home. Much like at our Kindergarten orientation long ago, we were told to let the practice using their lunch boxes, pencil boxes, opening their own lunch drink containers. Do the same with her gym bag. Make sure she is familiar with what is in there, which pocket the stuff is in. Learn to work in and out of the bag. So when warm up comes off it should go right into her bag, not on the floor.
And send her to gym practice with competition hair. To get her used to it and to make sure it stays put for the whole meet. Typically if it can withstand a full practice it will be fine for a meet.
Finally 10- 20 tee-shirts, warm up jackets, legging, capris, nike gym shorts, for the same gym, all look alike. If your meet stuff is not monogramed. Label your kids clothes. A sharpie with intials on the label works well. I spend most of my time at sign in, for our end of year program labeling the rec kids clothing as this is their first experience with a "uniform" usually tee shirts and shorts for march in.
As to what we keep in my daughters bag.
Water (yep she hates water fountains and I don't blame her) nice and cold, in her thermos.
Snacks (no nuts, we have kids at our gym with severe nut allergies). Again, snacks that will hold up and not get sticky or crumbly and make a mess, in a small bento type box with cool pack. Things like apples, grapes, beef jerky, turkey, salami,cheese sticks, maybe a hard boiled egg white with hummus, a bagel and cream cheese in quarters). She gets a few good luck Hershey kisses (not allowed to eat during meet, kids had a candy fest at a meet a few years ago, they were on a sugar high, coach almost had a stroke).
Tissues, napkins, hand sanitizer or travel wipes.
Hair brush, extra bun donut and scruntchies, bobby pins, hair ties/bands, travel size hair gel and spray. An extra leo (not comp leo cause I don't have an extra couple of hundred dollars sitting around).
Small first aid kit/rip kit, including tape grips if she rips. Lots of athletic tape.
Her Ipod now phone (which also contains a copy of her music, after compulsories, don't "assume" the person with the music will always make it, delays/illness happens) and ear buds.
Her USAG membership card.
PJs if the meet is going to be a late one. Change of clothes if its a long drive home.