We do not have an expert that deals specifically with laundry/cleaning issues, but our colleagues at Utah State University Extension have created a publication that provides recipes for homemade laundry detergents that might provide you with an alternative to bleach:
http://extension.usu.edu/files/publications/factsheet/FC_Clothing%26Textiles_2011-05pr.pdf

Good luck with your towels, and thanks for contacting Ask An Expert.