No, IIM Bangalore does not provide BBA program. If you are willing to pursue undergrad from IIM then you can opt for IIM Indore 5 year integrated course. The course combines both 3 year BBA + 5 year MBA. The Admission procedures starts right after class 12th. The entrance is taken by IIM Indore namely IPM entrance test. After entrance, interview is followed for those selected for the same. If you clear the interview also, you will get admission.

Best of luck.