As per the data available, there are 8 colleges in Bihar among which 6 are government and 2 are private offering BEd course.

Some of this colleges are:

Magadh University, Bodhgaya

Aryabhatta Knowledge University, Patna

KK University, Nalanda

Patliputra University, Patna

Nalanda Open University, Patna

For more colleges you may visit the link below:

https://university.careers360.com/colleges/list-of-bed-universities-in-bihar

To know more about BEd you may visit the link below:

https://www.careers360.com/courses/b-ed-bachelor-of-education

I hope this answer helps. All the very best for your future endeavors!