There is more than one way to arrive at any lighting result, but the way I described it above is how I would light it, with the equipment I actually own and am familiar with using, to get the exact types of beam spreads, and nature of the light.
ALTERNATE SCENARIO: Okay, say the main light option you have is a softbox: tape some black-out paper to it so the light that comes out is only down the center of the softbox, or tape some aluminum foil to it, to make a tall, narrow "strip light" that will project a tall, skinny beam.
Background light? Aim a speedlight at 1/8 power at a black background. Experiment so that you get a soft-ish sort of beam spread; The key is NOT to allow the light to rake across the background, but rather to have it impact the background more or less at right angles; maybe make a tinfoil snoot, and on the front of the flash, tape a piece of thick,clear plastic that has some messy, irregular blobs of duct tape on it, so the light that is projected is irregular. Think of the plastic bubble wrap that say, a pair of scissors comes in from Target, I mean that THICK and reallly tough stuff.
Hair light is very soft, and controlled. You could probably bounce a very weak, snooted light off the ceiling right above her, just out of camera range, and get a somewhat similar hair light. I do not know exactly what modifiers you have or what kind of light-shaping tools you have available to you. In B&W, you could probably use a continuous light as the hairlight, and shoot at whatever shutter speed needed to get the right brightness on the hair light. SAME goes for the background light as well; it could be lighted with...a desk lamp as long as the shutter speed is low enough to "burn in" the background light to the correct degree.
The shot you showed has very controlled lighting; that's where grids and diffusers and snoots and barn doors, used singly or together or in three-piece combinations mean being able to get things just so, without light blasting all over hell. The shot is not "just an umbrella lighting" kind of shot. It has a very narrow main light spread, a very small, soft hairlight, and the background has very little light on it.