If your betta likes to swim up to your finger and enjoy a gentle rubbing, this is just fine. You will need to be careful of a few things, however, so you don't hurt your betta through over-friendliness!
To start with, make sure your fingers are clean, and free from soap, hand lotion, perfumes or cleansers of any sort. While this seems obvious, it's easy to slip and forget from time to time. Wash your hands in hot water and use the friction of two hands rubbing together to clean them mechanically. Soap is not your friend here.
If you allow dirty fingers or any soap residue to enter your betta's water, try to make amends right away though a nice water change. Even a tiny amount of soap can make your little pet sick. Think of it this way - if you lived in a small room with recycled air, and someone came in chain-smoking, you'd have to deal with smoke-laden air for a very long time - until your air filters were changed. In the meantime, you'd be second-hand smoking. It's like that for a fish in a bowl or tank!
Back to petting your betta. You can try gently placing your clean finger in his bowl. Really friendly bettas that know their person will swim right up to that finger! From this point, you can GENTLY rub your finger along his side. He will probably rub you right back! Make SURE you are not using your fingernail, and don't rub too hard or for too long.
Even using the soft flesh of your fingertip will compromise a betta's slime coat. It's just what happens. The slime coat is the protective barrier that all fish need to keep stray microbes from taking residence in a fish's body.
You can help your pet by putting a few drops of a slime coat additive in your betta's water after you finish cuddling with him. The best dechlorinators have a slime coat additive in them already, so you can add a drop or two of Stress Coat, NovAqua, or whatever you use.
If your betta is not ready to be petted, leave him alone. Some bettas don't like it. Don't scare your friend by chasing him around the tank with your finger. Bettas have good memories - this is how they learn to recognize you as their feeder and caretaker. Give your betta time to come to YOU.
Lastly, don't let other people pet your betta, unless they know that person well and usually "flirt" with them (you know betta flirting when you see it). It's really not great to have your fish touched too much, even if he seems to enjoy it. Reserve that treat for yourself! :)
Betta Care - Caves and Hiding Spots
Buying Toys for your Fish
Betta Basics
Care for your bettas right!

