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B.A., Bachelor of Arts, Bachelor of Arts degree, bachelor’s degree
Abbreviation is all caps with periods. Note capitalization in other references

B.S., Bachelor of Science, Bachelor of Science degree, bachelor’s degree

B.C.E.
Before Common Era, sometimes used in place of B.C.

Bible, biblical
Capitalize and italicize reference to book, lowercase biblical

black
Lowercase in reference to race, preferred usage is African American

Board of Trustees, the board, the trustees
Capitalize specific body, lowercase for general references.