Hi notafish.
Yes, women do go fishing on their own!
My dad took all 10 (8 girls, 2 boys) of us fishing from a young age.
I took my 3 kids fishing from an early age and they all love it. I must add it's sea fishing, not that freshwater nonsense.
If you head down to your local library they will have a list of every club/society in your area. There must be something you have always had a hankering to try? It takes a leap of faith to go somewhere on your own, but nothing ventured, nothing gained.
I can highly recommend the W.I. It's nothing like you'd think - there's not a jar of jam in sight and they are not old, boring people. They go for meals out, visit interesting places, have guest speakers, try new things etc. You can go on your won and they'll make you very welcome! Our local group has members ranging from 25 to 75.
Good luck. xx