Hey Jaykishan

As far as I know you can take admission in any of the colleges or universities in Bihar after you do a diploma. Doing a diploma is not a hindrance in joining BSc at all. As log as you meet the eligibility criteria of the BSc course and the College's requirements. Generally the requirements for getting admission in BSc are:

10+2 or equivalent education

And the admission is usually merit based or entrance exam score based. All the best.