One of the most controversial topics in quilting concerns washing quilts. There are many right and correct ways to approach washing quilts. It boils down to what works for you and it doesn't have to be the same all the time. So here are some thoughts to consider and maybe a few points to contemplate.
Do you prewash fabric? That's easy. Yes and no! There are different qualities of cotton made for quilting. Independent quilt shops order from manufacturers and distributors using top grade base fabric most of the time. You can tell by the feel of the fabric, the number of threads and the quality of the dyes/printing colours. Chain stores often carry lesser quality fabrics that are thinner, stretchier and not as well printed.
Most fabric dyes on quality fabrics are stable and do not bleed when washed. There is sizing on the fabric taken from the bolt unless it is marked 'prepared for dyeing'. If you are concerned, then prewash the fabric to see if it runs and to remove the sizing that may irritate a baby's delicate skin. If a colour runs or bleeds, you can treat the fabric with a fixative like Retayne. I use it when dyeing fabric to set the colour and it works excellently. Soak the fabric in it for several minutes and no more colour comes out.