I'm a bit confused by Bob saying something like "Wouldn't it be cool if an electron had a field like a bar magnet?" ... Isn't that what it already has? In fact, isn't it a necessary characteristic of any charged particle with spin that it has a magnetic field? I know it's hard to imagine a point particle spinning, but that's quantum mechanics for you.
The magnetic field of an electron would be similar to that of a normal magnet. The quantum mechanical spin creates a magnetic field. All the field lines will curl back, none will continue into infinity. Usually you need moving charges for magnetism to arise. Typically, the electric field of an electron would be pictured as a bunch of evenly distributed arrows pointing from infinity straight into the electron. If the electron actually does have an electric dipole moment, then when you look really closely at the electric
field it should be slightly curved, but it will probably only be noticeable at a very small scale. I don't think it would completely close back on itself like a magnetic field would. If I remember Maxwell's equations correctly, you need a changing magnetic field to create an electric field like that. None of the field lines will close back on themselves, and some will go into infinity. I'm not sure what Bob meant. The electric field of an electric dipole does
look a lot like a magnetic field if you are close enough, even if there are some crucial differences in their overall shape.