B.A.M.S.

For the Government colleges the cutoff is around 40 percentile for SC category. Having 370 marks in NEET with SC category is good. You are eligible for the admissions, you can proceed with the counseling process. You can easily get admission in the Government colleges for BAMS and BHMS. NEET score is very useful for the admissions in Government colleges.

With a score of 400 in NEET, you have a fair chance of securing admission to a Bachelor of Ayurvedic Medicine and Surgery (BAMS) programme in Karnataka the cutoffs for BAMS courses can vary significantly depending on several factors including the category of the candidate (general, obc, sc, st), the specific college and the overall competition for the year.

YES you can even in that score you can try for MBBS as well as there is high chances that you will get a MBBS college as well which  could be a better career options as compared to BAMS 
karnataka is blessed with good clgs soo yes you can go for it if I come to know more about the BAMS course I will let you know in future.
if you are not getting a good government college for this marks for MBBS try for the lower government colleges but I would tell you to go for MBBS rather than going to BAMS

Admission to BAMS is mainly done based on NEET score. However, you can get admission for BAMS at some colleges like Ashtang Ayurved Mahavidyalaya, Bharati Vidyapeeth’s College of Ayurveda Katraj - Dhankawadi, Ayurved Mahavidyalaya, etc. with your grade in class 12th. The eligibility for joining BAMS is the candidate must have passed 12th with physics, chemistry, and biology as compulsory subjects and with at least 50% marks from any recognized board.