Efficient collection of photoluminescence arising from spin dynamics of nitrogen vacancy (NV) centers in diamond is important for practical applications involving precise magnetic field or temperature mapping. These goals may be realized by the integration of nanodiamond particles with optical fibers and volumetric doping of the particles alongside the fiber core. That approach combines the advantages of robust axial fixation of NV diamonds with a direct spatial overlap of their fluorescence with the guided mode of the fiber. We developed a suspended core silicate glass fiber with 750 nm-diameter nanodiamonds located centrally in the 1.5 µm-core cross-section along its axis. The developed fiber probe was tested for its magnetic sensing performance in optically detected magnetic resonance measurements using a 24 cm-long fiber sample, with the NV excitation and fluorescence collection from the far ends of the sample and yielding optical readout contrast of 7% resulting in 0.5 µT·Hz-1/2 magnetic field sensitivity, two orders of magnitude better than in earlier designs. Thanks to its improved fluorescence confinement, the developed probe could find application in magnetic sensing over extended fiber length, magnetic field mapping or gradiometry.