I haven't used India cotton, so can't comment specifically on that. However, what I would do in your situation is purchase tricot knit fusible interfacing. Fusing the tricot to the back of your fabric will give it body and prevent batting from peeking through. This is a technique that is helpful when working with old silk neckties.
I have found that fusible tricot is much less expensive when purchased from an online drapery company rather than regular fabric sites. The site I used is
http://www.bblackandsons.com . The tricot comes in beige and black, as I recall. I purchased a yard of fusible tricot from our local JoAnn's Fabric to compare, and I actually liked the one from Black and Sons better.
If you decide to use tricot fusible, it's a good idea to preshrink the fusible by holding a steam iron a couple of inches above it. After it has cooled, you can either lay your fabric on it or lay the fusible on your fabric to fuse the two together. Just make sure the glue side of the fusible is next to the wrong side of your fabric!
The advantages of using fusible tricot are: it is light in weight so doesn't change the hand of the fabric too much, it has stretch so doesn't make the fabric overly stiff, and I find it fairly easy to work with. It is great for giving substance to fabrics that would otherwise be too lightweight to use in quilts.
Mary