Thrifting for fabric doesn't always have to be just looking at old sheets. I've been able to source some sweet patterned 100% cotton fabrics in shirts (including Hawaiian and novelty patterns) and some homemade items (duvet covers, aprons, and dresses). Flannel shirts can also be an option if you want to look at rag-type quilts. You can also ask friends and family to pass on not-too-worn items - a shirt or cotton sundress with a food or wine stain on it isn't really going to sell, but could be cut up and put to use in a quilt.
There is an interesting journey described at
https://www.quiltedtwins.com/upcycled-blues-project.htm.
As others have mentioned, there is definitely a challenge with working with "what you find" rather than what you may actually want and it can take time to gather your materials. It's important to keep an open mind, get the creative juices flowing by seeing the amazing work done here and have a nice bit of storage space for all of your finds!