Hello Mayank, 

          As BBOSE (Bihar Board of Open Schooling Examination) is a recognized board, you're eligible to apply for DU JAT.

According to the DU JAT 2019 eligibility criteria, candidates should complete their higher secondary education in any stream (Science, Humanities, and Commerce) from a recognised board and obtain a minimum score of 60 per cent in four papers including English, Mathematics and other two subjects from the list of elective subjects as approved by the University of Delhi. 

Provided you have satisfied the eligibility criteria, you'd not have any problem applying for DU JAT'19.

I hope this helps answering your question.