Hello, Libby! Thanks for stopping by planDisney and asking your question!
Whenever I head to the parks, I always bring a bag with me! I like to be prepared with sunblock, snacks, water, an extra phone charger, and even a poncho for Splash Mountain. So, you can most certainly bring a bag with you to the Disneyland Resort. Keep in mind that your bag may be subject to search at security and that it can't be larger than 24" long x 15" wide x 18" high.
When it comes to riding attractions, you will simply bring your bag on board the attraction vehicle with you. For the most part, you will place the bag at your feet while you ride. The only attraction that I don't suggest you do this on is
Grizzly River Run as you and all your stuff will be soaked. Luckily, there are lockers near the attraction entrance that you can use to store your belongings for free for the first two hours. There are also
lockers located in both parks and the Esplanade that you can use all day for a small fee if you don't feel like lugging your bag around all day.
I hope this helps. Have a magical day!
-Linda