Bias is a partiality, an inclination or predisposition for or against something. The unjust and differential treatment of the members of different age, gender, racial, ethnic, religious, national, ability identity, sexual orientation, socioeconomic, and other groups at the individual level and the institutional/structural level that favor certain groups over others and has the effect of restricting opportunities for other groups.
Discrimination is usually the behavioral manifestation of prejudice and therefore involves negative, hostile, and injurious treatment of the members of rejected groups.
Racism is a form of prejudice that generally includes negative emotional reactions to members of the group, acceptance of negative stereotypes, and racial discrimination against individuals; in some cases it leads to violence.
Adapted from the APA Dictionary of Psychology definitions of bias, racism, and discrimination