After lugging my gear around in cloth grocery bags a few times, I decided to buy a proper bag to carry my stuff in. This is what I ended up buying:
About $70, a big, solidly constructed bag that opens in such a way that you can work out of the bag.
Room enough to fit my blowdryer, nozzle, concentrator, flat iron, 3 curling irons, all my scissors and combs, 4 different round brushes, 2 different flatbrushes, 3 different teasing/lacing brushes, a denman, pins, clips, elastics, nicknacks, the entire Bumble and Bumble product line, and an extension cord and power bar.
And it’s still something you can pick up and carry around. The wheels and handle are rugged, way more rugged than rolling luggage. Pretty sweet!