Usually state insurances covers ABA. If you do qualify for medicaid in your state, they have specialized plans for special needs that cover more services. I know here in Florida, state medicaid has "CMS" as a subgroup for special needs kids, and it covers ABA as well as diapers, pediasure, etc.

I have IEHP

Public schools should be able to provide ABA services at no cost under FAPE act (If eligible).