Is ionic bond just formed by "electrostatic" interaction between two oppositely charged ions?
You are absolutely correct that the electron has an angular momentum, which can be thought of like a magnetic field and which interacts with magnetic fields.
In "light" elements, however, the magnetic interaction is almost completely negligible.

The Hyperphysics page on the Zeeman Effect shows that in a hydrogen atom, a magnetic field of one tesla (which is fairly strong) splits energy levels by $5.78 \times 10^{-5} eV$, or roughly one-millionth of the ionization energy of a hydrogen atom.  

From just having done calcuations on the anomalous Zeeman effect for homework (you can use the formula in the link I provided and check it yourself), I can tell you that in a potassium atom, the energy levels of a p-electron split by 0.006 Hartree/Tesla, or 1/10,000 of the ionization energy of a hydrogen atom.

In other words, while there is a magnetic field (or what can be treated as one) generated by electron motion, it's fairly safe to ignore it in lighter elements.

As far as heavy elements go...well, you undergo what's called j-j coupling, caused by the fact that the electrons are going so fast that their motion becomes relativistic. To describe that motion requires the Dirac equation, which I have not studied in any level of detail. Instinct says that there are other considerations which are much more significant than magnetic interactions, but I have no proof whatsoever to back it up.