I bought the 10 gallon (XL) Ziploc Big Bags at Walmart. They're 2 feet x 20", and have a handle for carrying. Walmart didn't have them for a period of time, and I bought the XL bags at Dollar Tree. I found that the Dollar Tree bags ripped at the handle. I've never had the Ziploc Big Bags rip at the handle. It's gotten stretched a little, but not ripped. I think the Dollar tree bags were a little bit smaller than the Ziploc bags.
When Walmart didn't have them, I may have been asking for the wrong thing. I asked for project bags, but they're called "Big Bags." They come in L, XL, and XXL. The sizes of the other sizes aren't listed on the XL box. Our Walmart has the L and XL, and they're with the food storage bags. I think I saw some Hefty Bags, but they were smaller. I don't remember if they had a handle.
I keep individual, or similar projects in one bag. Then it's easy to grab and go. I have another one as a scrap bag, with some smaller ziploc bags with similar size pieces in them (1.5", 2", 2.5", and 3.5" squares, and another with the bonus half square triangles from making snowball blocks.). Another bag still has the leftovers from my hand-dyed quilt - it had the strips while I was making the quilt.