We demonstrate a high-sensitivity bidirectional magnetic field sensor based on a packaged optofluidic microbottle resonator (OFMBR) filled with magnetic fluid (MF). The relationship between sensitivity and different wall thicknesses and radial modes of OFMBR is theoretically analyzed. Then the thin-wall OFMBR is fabricated by etching a capillary with the fusion discharge process. The OFMBR and tapered fiber is packaged with a portable and robust coupling configuration. By applying perpendicular or parallel magnetic field directions to the OFMBR, opposite refractive index responses of the MF can be obtained, with resonant wavelengths redshifted or blueshifted as the magnetic field intensity is increased. A magnetic field sensitivity of 98.23 pm/mT can be obtained by using the second-order radial mode when the magnetic field is perpendicular to the packaged OFMBR. When the magnetic field is parallel to the packaged OFMBR, the sensitivity is -304.80 pm/mT by using the third-order radial mode and the detection limit reaches 0.0656 mT. The proposed sensor has the advantages of easy fabrication, high sensitivity, and reliability, showing a great potential in bidirectional magnetic field application.