Is there any alternative option in any other country where I can get into a master's program without requiring an MBBS degree in UK/Ireland for a Bachelor's?

Yes, you can apply for master's programs in healthcare-related fields in several countries without an MBBS degree.

Many universities in the UK, Ireland, Australia, the US, and other countries offer master's degrees such as Public Health, Healthcare Management, Health Administration, and Health Sciences. These programs typically accept applicants with a bachelor's degree in a related field - your background in Dentistry and work experience are usually considered relevant.

Admission requirements and accepted backgrounds vary by university and program. Some programs may also require relevant work experience or a strong academic record.