Hiii

BCA can be done from a private university as well as any govt university, also you can opt for distant learning
Private does not mean same as distant learning.
For a normal university program you need to regularly attend you classes at the university, make sure your attendence is not less etc. but in a distant learning program you are not supposed to attend the classes regularly either there is a fixed day in a week when you have to attend a class or there is no class at all. You would be given study material and assignments via courier and you have to study and complete assignments on your own and only appear for the exams at the designated exam center. You only have to make sure that your assignments are submitted on time.

Hope this is helpful. Feel free to revert back in case of any doubt.

Thanks!!