You should book a singles cruise with a singles agency. To be honest most women wont share a cabin with a complete stranger. If you book a singles cruise they will find you a same sex cabin mate, or you can pay extra and get your own cabin you will meet plenty of other singles.Therefore if you don't hit it off with one person there are more to choose from, better odds then taking a gamble with and unknown person in the same cabin I think.
New Single Guy, from one single male to another the odds are not in your favor in finding a single female roommate. Showcat is right about going with an organized single group instead of trying to meet one lady to spend anywhere from 3 to 7 or more days on a ship.
Even if you are lucky to get a female travel mate there is a possibility you might not get along at the beginning or in the middle of the cruise which could ruin BOTH of your vacations.
But if you insist on a female travel companion do what Pat suggest and go to "Seeking a Cruise Companion" on this site where you can post. Mind you I have never seen a single female post wanting to room with a single male.
Last advice, it is better for you spend the extra dough to have a room to yourself just in case you do meet that single lady.