Hello aspirant

You have not mentioned your category. But if you are from general category you may  get BDS seat with 371 score in private colleges. Which college you will get, depends upon cut off of the college. Cut off neet depends upon number of candidates appeared and qualified in exam, difficulty level of exam, previous year's cut off and availability of seats etc. Cut off neet for general Category is 685-145

You may try in  private Medical Colleges like

Kasturbha Medical College Mangalore

Kasturbha Medical College, Bangalore

MS Ramaiah Medical College, Bangalore

Hamdard Institute of Medical Sciences, New Delhi

For College prediction following link may help you

https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer