Before winding wire, particularly enameled wire, on a bare ferrite core, take steps to protect the wire from the abrasive ferrite’s edges and corners. If the core has an inside diameter of an inch or more, you can wind electrical or fiberglass tape on the core to separate the wire and the core.
The photo above is of a 2.4-inch core (OD) that has had a layer of Scotch 33 tape applied before winding the shielded cable around it. This is a sturdy coating that can be used indoors or outdoors.
If the core is smaller, you can use insulated wire, or if the enameled wires are twisted together, slip them through an insulating sleeve (vinyl or Teflon will do) and wind that on the core. If you use heat shrink tubing, use a heat gun to shrink the tubing onto the wires before winding. This avoids the risk of heat from the application causing the tubing to shrink in unpredictable (and possibly unexpected) ways while in use.