Would 15 gallons be okay?It all depends on the Betta and what size tank. I wouldn't have that many Neons with a Betta in any less than a 20 gallon.
I have 10 Neons in a heavily planted 20 long and have no problems with three of my four males. The first time I put the fourth male in that tank, he only lasted as long as it took me to net him.
BTW, I rotate three of the four between the 20 and a 10 gallon divided three ways.