When I want something that barely ravels, I use SewBatik fabrics. Yes, they are batiks, but they do have solid batiks to include a couple of different shades of red and white too (if you're looking for a white with a low-ravel factor as well). As with all reds, I prewash with a color catcher until there is no more red discharge and so far have not had a problem with bleeding after the quilt is made. If interested, you might purchase half a yard and see how you like it. SewBatik sells at shows but have an online business too. I have received orders very quickly and have never had a problem.
Here is a link to their website with a sample of one of their reds:
www.sewbatik.com/detail.aspx?ID=99.
Hope this helps.