Is denial of a transfer away from a biased supervisor an adverse action?

Yes.  According to the DC Circuit’s 2017 opinion in Samuel Ortiz-Diaz v. U.S. Department of Housing and Urban Development, No. 15-5008, “Although lateral transfers to different positions within a Department offering the same pay and benefits are ordinarily not changes in the “terms, conditions, or privileges of employment,” a discriminatory denial of a lateral transfer away from a biased supervisor can certainly be actionable under Title VII, given the adverse impact on the employee’s potential for career advancement. See Stewart v. Ashcroft, 352 F.3d 422, 426 (D.C. Cir. 2003).