BBA

Dear Nikhil!
You are in right direction. Yes, you can absolutely pursue MBA from any govt. institutions (I am not sure about private) after B.Com (H) from open, provided you need to clear cut-off and their GD/PI round. Now, come on to your 2nd query. As per me, that any college always prefer a full time graduate student (means going college regularly) rather than open students and you know very well, why! I am not demotivating you but that's the truth that they will shoot some questions that why you did your B.Com from open? Etc. but apart from these you can have a better representation if you impress them in interviews. It is totally no harm in doing B.Com from open but yes, it will be quite beneficial for you if you had your graduation from IPU in BBA because BBA is connected with MBA. So, at last, Nikhil! I would just suggest you that if you are thinking for MBA means you want to enhance your career but since you have did your graduation from open (which is less preferred). I think, first, go to gain some work experience for 2 or 3 years and then apply for MBA (it will give you a plenty of time to prepare for CAT-MAT or GMAT) it will give you a slight edge over other students from regular college.
I can understand that this answer is really too long to read but I hope that you found this helpful! Any query? Ask me anytime!
Best of Luck!