I am 71 and have travelled the world on my own for many years, as my hobby is snorkeling on coral, which means visiting tropical waters.
If the country or island is big enough, I hire a car to see as much of the hinterland as possible.
I live in a tiny ski resort in the French Alps, and use my home as a base for motoring all over France, Italy and Switzerland. When I was still quite glamorous, in my 40's and 50's, I did get some unwanted attention from men, but it is easy to make it clear that you are not interested. I went on a few singles holidays but sometimes they seemed to be full of desperate people - obviously not everyone! I spent one pleasant holiday with Saga, where there was a mixture of single people and couples.
I now spend two months of the French winter with my daughter in New Zealand, and I am enjoying exploring that beautiful country too. In January, I will be flying from New Zealand to Thailand for a week's snorkeling before heading home.
I don't seek conversation with other traveller, preferring to take a book or sudoku to dinner. I love the freedom of being alone, after so many years of holidaying with my daughters and my sister. I used to get mildly annoyed when taxi drivers or waiters would ask me where my husband was, which happened often in Malaysia, Egypt and the Caribbean, but I just put on a sad face and say I have lost him. In fact, I have been happily divorced for over 30 years.
After a lifetime of being totally non-sporty, I discovered snorkeling at the age of 58 when my daughter was living in Malaysia, and I then started trying to do something exciting every year, such as white water rafting in the Pyrenees. I have lost 20 lbs. since moving to the Alps last year, as I walk for several hours a day up very steep mountain paths.
The only time I have ever felt a little afraid to be on my own was when I lived in Chelsea and had to walk from the underground station in Sloane Square to my flat!
If you do actually want to meet other people, it is easier on your own, as when you are in a couple you tend to talk to each other most of the time.
My advice is to pluck up courage and set out on your big adventure. Life is too short to let fear hold you back.