Many males won't blow a bubble nest until the female is somehow introduced. There are a number of ways to do this, but in a 1 gallon tank, I would put a LOT of decorations in there, including something that floats, and see if things change over a 24 hr period.
When breeding bettas, be forewarned, you will have to spend a lot of time watching them very close so they don't injure each other. Their mating ritual can become quite brutal.
It is also not typical for a female to expel eggs. Usually the body will absorb them if they are not fertilized after a period of time. If it is truly eggs she is expelling, she will simply eat them and it won't hurt her. She'll produce another batch soon enough if her feedings are good and healthy.
Be forewarned BEFORE the breeding of your female is successful. They can have up to 100 fry in a spawn, and these fry need specialized food in order to survive. Be prepared to hatch your own artemia (baby brine shrimp) to feed them, they need extremely clean water, are very slow growing, but need to be seperated within the first couple of months... so each fish will need a container of it's own. I have had spawns of up to 90 fish survive at a time... this can be quite overwhelming to someone who isn't prepared, its a lot of work. Finding homes for them can also be a challenge. Pet stores won't take them until they are 6 - 12 months old because they are so slow growing and slow to get color. Most will stay a pale pink/peach color until well into the 4th month, and it can be hard to tell male from female before 6 - 12 months. Breeding bettas can be a lot of fun, but it can also get expensive and be a lot of work. Because the mating ritual is so stressful to both fish, if you are not intending to raise the fry, I woud NOT persue breeding. It is not uncommon for the female to sustain permanent injury during mating.
I hope this helps.