Tactoids are spindle-shaped droplets of a uniaxial nematic phase suspended in the co-existing isotropic phase. They are found in dispersions of a wide variety of elongated colloidal particle, including actin, fd virus, carbon nanotubes, vanadium peroxide, and chitin nanocrystals. Recent experiments on tactoids of chitin nanocrystals dispersed in water show that electric fields can very strongly stretch tactoids even though the dielectric properties of the co-existing isotropic and nematic phases differ only very subtly. We present a model for tactoids with a quasi bipolar director field characterised by a pair of virtual point defects, where the degree of bipolarness of the director field as well as the aspect ratio are free to adjust to optimise the sum of the elastic, surface and Coulomb energies. We find that tactoids do not elongate hugely in an external electric field, unless the director field is sufficiently strongly bipolar and somehow frozen in the field-free configuration. In that case, we do find reasonable agreement with experimental data. Results of Monte Carlo simulations support our conclusions.