How to clean a rope hammock?

I purchased a nice rope hammock last year and used for the summer. I stored it rolled up and just leaning against the wall in the garage for the winter. I pulled it out today and it is moldy looking. I put into the bathtub with soap and bleach but did not whiten up any. Does anyone have any product that can be used on rope to take the moldy, dark look out and the nice white look back?