IME (over 10 years working/spawning this species) the bubblenest is not always the best indicator of readiness to spawn in the male or breeding stripes in the female, some female don't have breeding stripes due to color, however, they can be good indicators too...just not always or for every Betta.
When breeders are separated without a way to get to each other you risk loosing the eggs/spawn, usually she will drop and eat them and you then need to wait at least 3 days and sometimes you will not know that the eggs have dropped and eaten and you can have trouble with the spawning or get weak eggs.
The best separator IME are plants...either live (best) or fake, crammed full to the point that it is difficult for the male to move through them, but the female can.
Most spawns will result is some torn fins and as long as the female can get away from the male to rest and hide all should be fine as long as she was properly conditioned and healthy to start, I would only worry if she is breathing heavy and become lethargic......... when she is ready she will go to the male in the head down position.
The male chasing and nipping the female is part of the spawning act or flirting and this gets them in the mood.
The hormones that are excreted by them will trigger the male to build the nest or pick a nesting site to draw the female to and the female eggs to ripen.
Soon the male will become gentler with her and slap her with his tail swimming in an "S" pattern toward the nest area and she will be in the head down position following him to the nest, sometimes he will turn on her and attack but she will return.... all part of the flirting game they play, then he will roll her over and embrace, they go into a trance, he recovers first as he floats down and she float to the top, often the first several embraces no eggs will be released and he may get frustrated and hit her or he can't get a good embrace and she hits him. But they will get the job done given enough time and that can be 2 hours up to 8 hours of active spawning.
Awesome to watch......I never get tired of watching the Betta spawning act....so graceful....I am watching one now as I type.......lol.....