Do not do 100% water changes every other day. By doing that your getting rid of good bacteria that betta's need to maintain good health
Cripes. I'm sorry, but in a 1 gallon bowl, there is NO hope of beneficial bacteria doing diddly squat for your fish in terms of cycling and bacteria don't live in the water column anyway. In a 1 gallon bowl, ammonia builds up fast
. Messing around with 40% changes will only help him be exposed to more ammonia. Aquakai had it right about 1 x 50% being okay, too, with 100%, but I'd be sticking with the 100% x every 2 days personally.
One of my fish is a chronically sickly little guy who can't have high water volume, is in 1.5 gallons permanently, and has had 100% changes every two days for 6 months. Sure, he stresses a little in his cup for 5 mins at water change time, but better that than swimming in ammonia! If my weedy little fish can cope, I'm sure yours can.
Vaccing a 1 g bowl just isn't worth the fiddling.
Put your fish in a covered cup (I use yoghurt containers that have been rinsed a LOT to spotless clean, no soap), tip the water in his bowl out, refill it with water to the correct temp, add conditioner. Spend a few minutes floating your fish in his cup in the bowl to equalise the temp, adding a little new water to the old every few mins. Let fish back into his bowl.
The vac will be very handy for the bigger tank, though!