You're absolutely eligible to pursue an MBA in Bangalore or Mysore even if you completed your Intermediate through APOSS (Andhra Pradesh Open School Society) and your degree through regular mode.

Most MBA colleges—whether affiliated to universities like Bangalore University, VTU, or Mysore University—primarily require a recognized bachelor’s degree with at least 50% marks (45% for reserved categories). Since you've completed your graduation through regular mode from a recognized university, that fulfills the key eligibility.

Your APOSS qualification is also valid as long as it’s recognized by the government and education boards, which it is. It might raise minor documentation or verification questions during admission, but it won’t disqualify you. You should carry all necessary original certificates including your APOSS pass certificate, transfer/migration certificate, and degree marksheets during admission or counselling.