Yes, you can get a private seat for BAMS with a NEET UG Score of 250 (under General Category).

Here I am sharing with you some statistics (NEET UG 2020) regarding BAMS Counseling in Karnataka -

(1) BAMS Closing Rank in Karnataka for the first round was 3,54,298 under AIQ 15% category  .

(2) BAMS closing rank for the second round  was 3,85,571 rank under AIQ 15% category.

(3) BAMS Closing Rank for Ayurvedic colleges in Bangalore was 2,86,205 rank in 1st round  and 3,19,447 rank in 2nd round.

Alternatively, to get a list of all colleges ( AYUSH) you can get via All India Counselling with your rank and score, you can use the College Predictor Tool - NEET College Predictor 2021 - Predict Colleges based on your Rank (careers360.com)

To get complete details regarding AYUSH Admission, you can visit the link - Admission to AYUSH courses through NEET 2021 - Dates, Registration, Process (careers360.com)

Hey aspirant. Hope you are doing well.

Unfortunately, with your scores, you won't be able to get a private seat in BAMS. The minimum neet scores required for admission in Private institution for BAMS course is 180. Adding to this, you belong from general  category. This makes it much harder.

Please don't put yourself down. All the best.