Several years ago I attended a SAGA convention and learned to make this super simple baby bonnet from a tea towel.
Isn't this just adorable? It is made from the pattern Pricilla's Layette by Jeannie Baumeister of Old Fashioned Baby, which seems to be discontinued. However, the Scaque, Wrapper and Embroidery Designs looks as though it would work. It is available on Jeanie's website. The pattern requires a 12 - 14 inch wide tea towel, ours had this lovely cutwork on the edge. We used silk ribbon for the gathers in the back and for the rosettes and ties in the front. A year or two after this class, Sew Beautiful Magazine published a article by Jeannie describing just how to not only make the bonnet but a complete sacque as well. The sacque requires four tea towels, but it can be pretty difficult to find five matching tea towels. You could probably get away with using three matching towels for the bonnet and fronts, then two other matching towels for the back. This was published in Issue No. 99 which is no longer available, but you can find it on ebay from time to time.
Doesn't this make a lovely, sweet gift? And quick to make; you could make several in advance to have on hand when you need a quick gift.