Yes you can get BAMS private easily.

Dear Candidate

See as per your Marks-250 it is difficult to get a Government Medical Seat even if you have a state quota and another quota if applicable. You should have maintained a score above 550 to be on the safer side.

You cannot get into any medical college with this mark.

Also, 250 is a very low score even for securing admission into BAMS course.

At this stage, I will suggest you must use this link to get a fair idea about the colleges both Private and Government you can get as per the score you have received and then plan accordingly.

https://medicine.careers360.com/neet-college-predictor

 You may try for private colleges where The rank up to which a college will it will offer a Medical MBBS Seat depends upon the College itself and varies from college to college. You must enquire it from the college you desire to seek admission into.