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Some of the top MCA colleges of Bangalore are:
Christ University, Presidency College, RV College of Engineering (RVCE).
You have to check whether they provide MCA-part time.
But i would recommend you to join for regular MCA from some top institute like Christ University, Pune University, Lovely Professional University.

Yes you can change your stream by taking admission in BBA

Management courses like BBA and MBA require significant mathematical and analytical skills. Math skills covered in a Commerce curriculum should suffice. You may not use some of the advanced concepts of calculus in a management curriculum.

You can walk in to get the MBA admission. The classes will start from august 5th. So its better to get admission before that.