It can be so rewarding, yet so frustrating to breed bettas. I agree that the one gallon tank is probably too small. It's normally recommended to use at least a five gallon. I, personally, use a ten gallon about half full, plenty of hiding places, a sponge filter set up, but not turned on until after eggs hatch. The water temperature is also an important factor and should be kept at about 82 degrees.
Conditioning is also an important factor and that doesn't include just what you feed them. I have found in most cases that it's best if the male and female don't see each other 24/7. When I'm conditioning a pair, I put them in separate tanks side by side with paper or whatever will fit that I have on hand between the tanks, which I remove several times throughout the days for anywhere from 15 minutes to a half hour. This allows them to flare and dance at each other, but doesn't give them an opportunity to grow bored or used to each other. During this whole process they are also fed small portions of a variety of food three times a day.. this ranges from frozen foods, live foods and their normal betta bits as well as thawed peas. Normally I condition for a minimum of three weeks, though there have been times when I was anxious and tried to breed them sooner.
That's just the preparing part. There's always the possibility that one or the other just may not like the other. I had a pastel pair that frustrated me to no end. They actually split the breeding tank themselves. One stayed on one side and the other stayed on the other side. They only chased each other if one ventured into the other's side and they never bred. They more or less co-existed in the tank but had no desire to spawn with each other. I put in a different female after conditioning her and had a spawn within hours.
I know you said the airstone is on the female side of the tank, but is the surface water moving on the male's side? If it is, that may be why you're not seeing a bubblenest or it could be that he just isn't a good bubblenest builder. Some males only build a nest during the actual spawning while others never build one and just get the eggs to stick to the side of the tank at the surface. It will look like a bunch of bubbles packed against the glass. If there isn't anything on the surface for him to attach the nest to, it may just be a line of bubbles going along the glass.
A spawn can have up to 500 eggs, but that doesn't mean that all of them will hatch.
The most important thing and probably the hardest is having patience. I have never had two spawns that were exactly the same even when I used the same pair more than once, but with a little experimenting and practice, you'll learn what works for you and your bettas and will begin to have successful breds.