My new betta lives in a 1.5 gal bowl (I know - not ideal - but its what I have and I'm taking good care of him!). The water needs to be changed regularly but I keep reading how you shouldn't use a net to transfer bettas because of fin damage. If not a net, then what? I used a plastic cup the past few water changes but that seems kinda traumatic too.
If you're careful with the net, it should be fine. I never have had any issues! Just don't pin him in a corner with it so you don't scrape him or anything. You have to be very gentle. It also helps if you soak the net in treated water for five minutes beforehand to soften it up.
A cup is good because it kind of sucks them up into it and there's less risk of scraping them with it. It's definitely more gentle than a net. Your fish is going to be really scared and traumatized until he gets used to the routine. But it's better than being in gross water!
Some people can use their hands and bettas will swim into your hand as they get used to you (I was so happy when mine did the first time!)... but I'd be careful because he can wriggle out and fall on the floor or whatever. You'd have to place him straight into a cup.