Context. Phosphorus-bearing species are essential to the formation of life on Earth, however they have barely been detected in the interstellar medium. In particular, towards star-forming regions only PN and PO have been identified so far. Since only a small number of detections of P-bearing molecules are available, their chemical formation pathways are not easy to constrain and are thus highly debatable. An important factor still missing in the chemical models is the initial elemental abundance of phosphorus, that is, the depletion level of P at the start of chemical models of dense clouds. Aims. In order to overcome this problem, we study P-bearing species in diffuse and translucent clouds. In these objects phosphorus is expected to be mainly in the gas phase and therefore the elemental initial abundance needed in our chemical simulations corresponds to the cosmic one and is well constrained. Methods. For the study of P-bearing chemistry we used an advanced chemical model. We updated and significantly extended the P-chemistry network based on chemical databases and previous literature. We performed single-pointing observations with the IRAM 30 m telescope in the 3 mm range towards the line of sight to the strong continuum source B0355+508 aiming for the (2–1) transitions of PN, PO, HCP, and CP. This line of sight incorporates five diffuse and/or translucent clouds. Results. The (2–1) transitions of the PN, PO, HCP, and CP were not detected. We report high signal-to-noise-ratio detections of the (1–0) lines of ¹³CO, HNC, and CN along with a first detection of C³⁴S towards this line of sight. We have attempted to reproduce the observations of HNC, CN, CS, and CO in every cloud with our model by applying typical physical conditions for diffuse or translucent clouds. We find that towards the densest clouds with v_LSR = −10, − 17 km s⁻¹ the best-fit model is given by the parameters (n(H), A_V, T_gas) = (300 cm⁻³, 3 mag, 40 K). Conclusions. According to our best-fit model, the most abundant P-bearing species are HCP and CP (~10⁻¹⁰). The molecules PN, PO, and PH₃ also show relatively high predicted abundances of ~10⁻¹¹. We show that the abundances of these species are sensitive to visual extinction, cosmic-ray ionization rate, and the diffusion-to-desorption energy ratio on dust grains. The production of P-bearing species is favored towards translucent rather than diffuse clouds, where the environment provides a stronger shielding from the interstellar radiation. Based on our improved model, we show that the (1–0) transitions of HCP, CP, PN, and PO are expected to be detectable with estimated intensities of up to ~200 mK.