No, your assumption that “some other race” means you “don’t qualify for bi-racial” is wrong. “Some other race” means you don’t identify with any of the racial c

No, your assumption that “some other race” means you “don’t qualify for bi-racial” is wrong. “Some other race” means you don’t identify with any of the racial categories on the Census, and in practice that means you’re Hispanic/Latino or Middle Eastern - those groups are officially grouped into white, but respondents often don’t identify that way. If your grandparents were biracial you’d be biracial.