The stack composition in trilayer Planar Hall effect bridge sensors is investigated experimentally to identify the optimal stack for magnetic bead detection using the sensor self-field. The sensors were fabricated using exchange-biased stacks Ni80Fe20(tFM)/Cu(tCu)/Mn80Ir20(10 nm) with tFM = 10, 20, and 30 nm, and 0 ≤ tCu ≤ 0.6 nm. The sensors were characterized by magnetic hysteresis measurements, by measurements of the sensor response vs. applied field, and by measurements of the sensor response to a suspension of magnetic beads magnetized by the sensor self-field due to the sensor bias current. The exchange bias field was found to decay exponentially with tCu and inversely with tFM. The reduced exchange field for larger values of tFM and tCu resulted in higher sensitivities to both magnetic fields and magnetic beads. We argue that the maximum magnetic bead signal is limited by Joule heating of the sensors and, thus, that the magnetic stacks should be compared at constant power consumption. For a fixed sensor geometry, the figure of merit for this comparison is the magnetic field sensitivity normalized by the sensor bias voltage. In this regard, we found that sensors with tFM = 20 nm or 30 nm outperformed those with tFM = 10 nm by a factor of approximately two, because the latter have a reduced AMR ratio. Further, the optimum layer thicknesses, tCu ≈ 0.6 nm and tFM = 20-30 nm, gave a 90% higher signal compared to the corresponding sensors with tCu = 0 nm.