Aims: The B fields in OB stars (BOB) Collaboration is based on an ESO Large Programme to study the occurrence rate, properties, and ultimately the origin of magnetic fields in massive stars. Methods: In the framework of this program, we carried out low-resolution spectropolarimetric observations of a large sample of massive stars using FORS 2 installed at the ESO VLT 8 m telescope. Results: We determined the magnetic field values with two completely independent reduction and analysis pipelines. Our in-depth study of the magnetic field measurements shows that differences between our two pipelines are usually well within 3σ errors. From the 32 observations of 28 OB stars, we were able to monitor the magnetic fields in CPD -57° 3509 and HD 164492C, confirm the magnetic field in HD 54879, and detect a magnetic field in CPD -62° 2124. We obtain a magnetic field detection rate of 6 ± 3% for the full sample of 69 OB stars observed with FORS 2 within the BOB program. For the preselected objects with a v sin i below 60 km s-1, we obtain a magnetic field detection rate of 5 ± 5%. We also discuss X-ray properties and multiplicity of the objects in our FORS 2 sample with respect to the magnetic field detections. Based on observations made with ESO Telescopes at the La Silla Paranal Observatory under program ID 191.D-0255(E,G).