I’ll give you the same advice I’ve given my sister, who is in her mid-40s and just finalized her second divorce this past fall.
Don’t make your end goal be a committed relationship. Because you’re not comfortable with random hookups/flings, just make your goal to make some new friends, male or female, doesn’t matter. Don’t be looking for your next boyfriend. Join meetup groups, put a profile on one of the free internet dating sites, and you set the terms for yourself, based on whatever you are comfortable with. Know that not every date will end up with a meaningful connection. It doesn’t have to be ugly drama either. Put it out there right up front that you are looking to make new friends, period.
What can happen (I won’t say what WILL happen) is you will make some friends. They will introduce you to other friends. One day, you may notice that you aren’t as invisible as you think you are. While you are making all these friends, you will be working through your issues/baggage from your marriage. By the time you meet a Special Someone (that evolves from a friendship to something more), you may have worked out your insecurities or fears or whatever so that you present yourself as a whole, healed, healthy person who would make a good partner for someone. Right now, you are probably still sorting yourself out somewhat (depending on how amicable the split up was).
You are not anywhere near your expiration date. Plenty of people get together in their late 30s or early 40s or older. Right now, focus on you. Who do you want to be in a relationship? What do you have to offer to your next relationship? This is the time to experiment with new looks, get back into the gym, start working on hobbies and things you’ve always wanted to try, but did not for whatever reasons. Be the awesome person you want to become and you will be irresistable to someone who is looking for a mature woman who has her head on straight. Focus on making friends and getting your head screwed back on nice and straight, the relationship part will grow out of that (probably) new pool of friends.