Theoretically any EM (electromagnetic) field would have an electric-E field and a magnetic-M field, that can be measured somehow.
Magnetic field have the highest magnitude in the reactive near-field of the antenna (in the proximity of the antenna).
Generally the magnetic filed of a dipole, or a monopole, or a patch antenna is low. Those antennas have good far-field EM radiation.
The greatest magnetic field is provided by loop antennas, which usually are not used in Bluetooth communication, due to their poor far-field radiation.