BDS

If you want admission to government colleges for BDS and BVSC courses, then you can not get admission on your NEET score.
1- The minimum marks in NEET to get admission in a Bachelor of Dental Surgery BDS are 450+ for the General category.
2- The minimum marks in NEET to get admission in a Bachelor in Veterinary Science BVSC are 350+ for the General category. However, you have not mentioned the state you belong to that's why I provide general data because the cutoff varies from state to state. If you want admission to a private college for the BDS and BVSC course, then you can get direct admission. For direct admission, there is no need for a NEET score.

New counseling Rules:
The Medical Counselling Committee of Directorate General of Health Services, Ministry of Health and Family Welfare has developed software for all the participating states/counseling authorities for NEET-UG/PG to upload the names and roll numbers of students who have joined up to second round and further rounds of the state quota or second round of the All India Quota on the common portal. These joined candidates up to the second round of All India Quota or State Quota shall not be eligible to participate in the further rounds for All India Quota or for State Quota from the academic year 22-23 onwards. For more counseling details, you can visit the link (https://ask.shiksha.com/q-qna-7106245). Cut-off for government BDS colleges: Based on the 2021 year cut-off, to attain a Bachelor of Dental Surgery BDS seat in a government dental college, a candidate is required to score a minimum of 450 marks in NEET Under 15 percent AQI, you need to score more than 480 marks in NEET to get a seat in BDS College. I hope this will help you.

According to your marks, you can get admission into the Koppal Institute of Medical Sciences, the only government college in Karnataka for the MBBS course. For a dental course, you can get admission into the Government Dental College and Research Institute, Bangalore. A list of private colleges in Karnataka which provide MBBS courses
1- JJM Medical College.
2- Jagadguru Gangadhar Mahaswamigalu Moorsavirmath Medical College.
3- Sri Devraj Urs Academy of Higher Education and Research
4- Jawaharlal Nehru Medical College, KLE Academy of Higher Education and Research
5- Sapthagiri Institute of Medical Sciences and Research Centre
A list of private colleges in Karnataka which provide BDS courses
1- A. Pandu Memorial R. V. Dental College
2- Krishnadevaraya College of Dental Sciences and Hospital
If you want more information regarding the college, course, or anything else, kindly visit the link (https://www.shiksha.com/medicine-and-health-sciences/neet-college-predictor). This information is based on the 2021 NEET cutoff results. For this year, the results may be different. I hope this will help you.

It is difficult to accurately predict in the absence of your category-based rank; however, based on the previous year's trends, it has been observed that you have to score more than 400 in NEET UG to get a government quota seat in Karnataka. With a score of 306, you may get into a Bachelor of Dental Surgery college, but you will get a private seat. For instance, you may get admission into dental colleges like the S. J. M. Dental College and Hospital under private quota seats. Alternatively, you can also use the Shiksha platform's NEET College Predictor 2022 (https://www.shiksha.com/medicine-and-health-sciences/neet-college-predictor) to get more specific recommendations of colleges you may get with this rank. To get a list of possible colleges, enter your NEET rank, gender, category, and domicile here.

Hey,
I am one of the best examples that you can relate to.
I've done my BDS and worked in a clinic for an year. Then gave my CAT, XAT, SNAP etc, and scored a whooping 97.36 percentile. I am currently an alumnus of XIMB-HR working in Jodhpur.
I also had a dentist amongst my seniors and one among my juniors in PG. A junior dentist gave her CAT and scored 99.2 and is an alumnus of IIM Calcutta. She didn't like being a dentist too.
Campus placements are good if you are good with your presentation skills, communication and are diligent enough. If you have a love for it, broaden your horizons, you need not stick to MHA nor think that you have wasted 5 years. It, infact, is a unique factor and helps you to get noticed.
As for me, I've never regretted choosing this path because just like you, I've always dreamed of being associated with big companies. Following your passion might not be always possible but doing what you dont like is something you might have to live with regretting for the rest of your life. Choose well.
All the best!!
Edit: An year after my MBA, I have now moved to my home state, working with Accenture. Your hardwork will pay.

Think DDS/ DMD or the residency in dentistry would be the best option to study abroad post BDS. As unlike in India, dentistry is one of the most respected profession in western world. Amongst the option you have provided I. e. Maharashtra or MBA or MS Healthcare administration, I would suggest you to go for the better university than degree. As all the above mentioned degrees will train you for the same skill Sets. Also, if you're considering the US as an option to pursue your higher education then try to inquire for a course that comes under STEM. As you will get 3 year optional practice training (OPT) post STEM course and you will get only 1 year OPT post non STEM course. Cheers!
PS: I could have helped you in a better way, if you had provided me countries you're considering for your higher education.