[Richard777 (OP)]

The four quantum numbers (n, L, m_L, m_s) are well defined in the literature.
Where;   m_s is magnetic moment associated with spin; m_s = ±½  (spin up, spin down)

It is reasonable to assume that the rotation of a bound electron may set up a magnetic dipole. If a magnetic dipole does exist then the magnetic moment “associated with orbit” (m_n) may have two possible values;
      m_n = ±½   

Where;      
m_n = -½ represents “dipole north”
m_n = +½ represents “dipole south”

Does a bound electron have orbital magnetic moment?

[chiralSPO]

Just to be clear: electrons don't actually orbit the nucleus--early models treated the electron-nucleus system like a mini solar system, but further experiments proved that this cannot be the case. We still talk about "orbitals" but this doesn't actually mean that the electrons are going around the nucleus in any sort of predictable pattern (or that they have any well-defined position at the scale of the nucleus.

It is possible for electrons in atoms to have a net angular momentum, and this is described by L and m_L terms.