The Bohr model is a phenomenological model in analogy to the planetary model. The electric field is a part of the electro magnetic field. Qualitatively, a negative charge orbiting a positive charge is expected to emit electromagnetic radiation , and in the classical model it is expected they will fall on each other. The data Bohr fitted, the Lyman and Balmer series, showed a discrete spectrum for hydrogen, not a continuum.
In such a model the stability of the orbits has to be postulated, that the electrons could only radiate in transition between fixed orbits in discrete steps corresponding to the observations.
So in a sense the model goes beyond classical electromagnetism, and it needed the development of quantum mechanics and quantum electrodynamics for mathematical accuracy in modelling atoms.