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Yes, there are many institutes offering 1-year PG courses. Check the below link: https://www.shiksha.com/business-management-studies/colleges/executive-mba-colleges-india
While a Bachelor's degree demonstrates proficiency in an academic area, a Master's degree signifies expertise. It is employment-friendly. If you are already a member of the workforce, taking two years off for graduate school can seem like a lengthy tenure. One year, however, affords you the same opportunity for advancing your career without missing two years of working. The 1-year course is more cost-friendly than the 2-year course. Master's degree can be an invaluable differentiator in a crowded and competitive job market. While adding skills, job responsibilities and other talents add appeal to your resume, a Master's degree is more than a mere line item. Even if it was possible for a one-year Master's degree to convey as much knowledge and expertise as a two-year program, the pace will be significantly faster.

You should not get disheartened by one failure. You must try hard to clear all the exams in BBA with good scores. Because in future while looking for jobs in the corporate world, a good graduation mark sheet matters a lot. After BBA, you can go for MBA. Most of the first year courses of MBA are in line with BBA course curriculum. Depending on your field of interest, you can choose a specialization. MBA students are paid well in the industry. MBA is more about practical application and less of theoretical knowledge. So, students didn't perform well in graduation but with good analytical skills and smartness excels in MBA. While a Bachelors degree demonstrates proficiency in an academic area, a Master's degree signifies expertise. There are practically infinite Master's degree options available around the world. In fact, whatever your interests or career aspirations, there is a program that will work for you. However, it's not just a matter of deciding on a discipline.