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. In the framework of this programme, we carried out low-resolution spectropolarimetric observations of a large sample of massive stars using FORS2 installed at the ESO VLT 8-m telescope. 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 3sigma errors. From the 32 observations of 28 OB stars, we were able to monitor the magnetic fields in CPD-57 3509 and HD164492C, confirm the magnetic field in HD54879, 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 FORS2 within the BOB programme. For the pre-selected objects with a v sin i below 60 km/s, we obtain a magnetic field detection rate of 5+-5%. We also discuss X-ray properties and multiplicity of the objects in our FORS2 sample with respect to the magnetic field detections.