A bidirectional circularly polarized (CP) double asymmetric periodic leaky-wave antenna (PLWA) with wide 3-dB axial ratio (AR) bandwidth is presented. It is the first single-layer bidirectional CP PLWA with the same handedness in both half-spaces being reported. It consists of cascaded all-pass phase inverters hosted by a double-sided parallel stripline. A simplified unit cell facilitating theoretical analysis is first investigated, and both design rules and a radiation model for CP radiation are deduced. In particular, the phase quadrature and its weak dependence on the zenith angle, the origin of the same handedness in both half-spaces, are justified. Then, a practical unit cell design, suitable for PCB fabrication, is proposed, and a 30-cell PLWA prototype for the sub-6-GHz band is designed and fabricated, which exhibits a 10-dB return loss bandwidth from 4.5 to 7.0 GHz. Although the transitions feeding the antenna and the fabrication imperfections perturb the radiation, mainly in the upper half-space, the prototype matches the simulations from 4.6 to 6.9 GHz, corresponding to scanning from +45 to 34 in the lower half-space. The measured realized gain ranges from 4.4 to 6.6 dBic in the operating band. Meanwhile, the axial ratio of the scanning beam remains below 3 dB throughout the 40% bandwidth.INDEX TERMS Circular polarization, double-sided parallel striplines, leaky-wave antenna, phase inverters, the same handedness.