Once the state prepare their state ranks, they will call for counselling. Depends on your own state government. It's mostly expected to start in the last week of June or the first week of July. 

For BHMS offering government or private colleges, every institution/state having their own system. There is no any centralised counselling for that as of now. You have to apply for particular college or state government colleges through their own procedure. Every BHMS college would consider only NEET score for the purpose of counselling. Check you state government official medical education website for more information. Apart from that you can go through private colleges website as well who offers BHMS course.

Good luck