Just a note, if you have a clean enough cup, such as the ones pet stores sell the bettas in, you can submerge the cup to draw the fish into the cup (hold it at an angle with some water in it.
This way you have it in water it is adapted to, and are not stressing it by contact with the net, more its being pulled down by water current. Only issue is that with certain tanks it may be difficult to do, so you may want to run your arm under cold water for a bit, in the event you must dip in with the cup. I mean, you see in the videos that the source breeders put their hands in the water. It is OK as long as you keep your arm and the water clean of chemical or your sweat, short term, and the cup is clean and large enough for the betta temporarily. Then bob it in the hold tank for a bit and submerge and tilt to release him calmly into the water.