My preference also would be to wash it after it is quilted, even if it is stained. If it smells, I would just hang it outside for a few days.
If it absolutely *must* be washed before quilting, I would machine baste it thoroughly to muslin, wash it by hand, and iron flat while still damp. Fabrics that are not stabilized to batting by means of quilting can shrink disproportionately to each other. This method should allow stretching of any shrinking-distorted fabrics back to where they need to be. It also reduces fraying of the seams.
There is still the risk that some fabric will bleed. To minimize this, I would probably do the washing in a large top-loader with lots of water. Do not allow to agitate; turn off the machine after it fills with water and hand agitate by pushing down with your hands. With enough water, any bleed is likely to be diluted enough not to land in other fabrics. If you do get some bleeding, just leave it alone until the top is quilted. During the first washing of the quilt use a large-capacity washer (lots of water), hot water, and Synthrapol. That will be likely to remove any unset dye bleeds.