Glute brigdes do not in isolation reduce strain on the hamstring.
Hip flexor training and glute bridges can significantly increase strain on the hamstrings (biceps femoris more specifically) if they cause excessive external rotation of femur and decreased posterior pelvic tilt of the pelvis at terminal knee extension.
What will reduce strain on the hamstrings is progressivly increasing speed and volume of sprint training and increased posterior pelvic tilt and adduction, internal rotation of the femur at terminal knee extension. Also eccentric training of biceps femoris with glute ham raises or nordic hamstring.
How does adduction and internal rotation of the femur reduce strain on the hamstrings at TKE? Are you saying it takes it away from BF and puts it a bit more on adductor magnus?