Although I am married, I've done more than half of my cruises without my husband (he doesn't like sea days, and I love them). I have never been bored or lonely on a cruise ship.
Cruising is the PERFECT way to travel for a woman alone. People on cruise ships expect to interact with strangers. Based on your self-description, my advice to you would be to pick a one-week cruise out of a port that is relatively convenient to you, on either Holland America or Celebrity. Don't buy it, just pick one from their websites that sounds interesting to you; then post here looking for a companion for that specific cruise. Maybe you'll find someone else who's interested; if not, you haven't lost anything. If you do, exchange e-mails and if possible phone calls until you feel you are comfortable with whoever it is. Then you can both go ahead and book the trip, each giving your payment information separately to whatever agent you are using.
While you are waiting for a possible companion, talk to a few travel agents and see if you can find one you're comfortable with, who seems to know something about cruising (perhaps he/she could suggest an itinerary good to start with). You will not pay any more for a cruise if you use an agent than you would booking directly with the cruiseline, and in fact the agent might throw in a minor perk, like a bottle of wine in your cabin. In particular, ask if the agent could keep you informed of any singles specials that might come up. I've paid as little as $75 over the individual rate for 2 in a cabin, to have the cabin to myself; and that was for a 15-day cruise. The extra space is nice, and I still get lots of interaction with others during the day.
HAL seems to have more "specials" than Celebrity, but if you should happen to fall in love with cruising Celebrity has a much better loyalty program.
You should have no problem at all meeting others and making friends-for-the-trip. Just smile and say something friendly to anyone you happen to be near. It is incredibly easy to strike up a conversation with someone while you're waiting to board, or sitting in a lounge chair next to the pool, or walking around the deck, or on a shore excursion. And an interesting phenomenon is that anyone you speak with the first day, you'll probably run into almost every day. Unless they're traveling with a group, people expect to be seated with strangers at meals; it can be part of the fun. And particularly at breakfast in the buffet, asking a person sitting alone or a couple at a table for 4 or more if they are expecting others, or would mind sharing their table, is quite normal. Do you play trivia or golf? There are putting contests and trivia challenges on just about every ship. Those and the communal jigsaw puzzles are a great way to meet others. If you do any kind of needlework, speaking with someone you see knitting or crocheting or whatever is very comfortable; and there's ALWAYS someone working on something, especially on sea days. Some ships even schedule get-togethers for needle workers. Many also offer some sort of lessons, which is another way to meet people. I've done tai chi, origami, and lei making on ships, and learned how to play mah jong. There are usually bridge and often scrabble groups.
Give it a try, and if you have any questions, you've found the right place to get an answer for them.