Cut a Square from String Pieced FabricPress the fabric with a hot iron. We don't usually tug on our quilting units, but this is an exception. Use steam and a bit of pressure to make sure all loft hidden in seams is fully pressed. You'll probably need to press seam allowances to one side.
Fit one of the triangles around the dog's neck. There should be plenty of overlap for attaching a Velcro closure. Fold the bandana back a bit along the long edge to make a narrow collar and fit it again. Does that look better? If it does, you can create a collar later.
This isn't rocket science, so feel free to take your scissors or rotary cutter to the triangle to make it a better fit along the dog's neck or back.
Clip the Seam AllowancesUse special rag quilt scissors (or any sharp shears) to make a series of cuts straight into the seam allowances, taking care to stop before you reach a seam. Make a cut about every 1/4". Be careful not to cut away chunks of fabric at angled ends where strips are pieced together.