How to get the high-contrast white background effect?

Oops, sorry that was the wrong picture...this is the one I mean:

Can you post an unaltered image so we can see what the actual lighting & exposure looks like? My guess is that you're not throwing enough light on the background, but I'd like to see for sure.

Also, you're in full manual mode on the camera, correct?

Yeah, you simply need more background light. If it's B&W only, depending on the background material (paper?), you could even through some lighting behind the BG and let it diffuse through.

If you're getting a color cast in the BG, you're probably not exposing it enough, otherwise you would get a neutral white from the light, not something the light is bouncing off of. Just increase your lighting ration between subject and BG. Like a lot of photographers, I always set up my background and exposure before I move to the subject anyway.

Not enough light on the background. In the image you show here the gray looks about like a zone V or zone VI medium gray. You want it to be at least 2-3 stops brighter to wash out to pure white, so that means more light. Exposure time (=shutter speed) is not relevant unless you are relying on ambient light as well as your softboxes, as long as you are shooting at or slower than your camera's maximum sync speed. Be sure, as someone else advised, that your camera is on manual exposure control as well.

Your softboxes, while adequate for a single-person headshot, may not be large or powerful enough to generate enough spill to light the background properly, especially if there is some distance between model and background.

Short answer is, light the background separately. Maybe you could try one softbox on the model--very close, just outside the image frame--as key, a reflector or two for fill, and your second light, with or witthout softbox, lighting up the background.

Yes, I'm allowing the camera to choose the shutter speed aperture automatically. Which of these should I be setting manually?

Also, the reflectors (aimed at the background) are positioned about three feet off the floor about 1-2 feet from the (paper) background. Is that a good distance/height?

Sorry but I don't have a copy of the unaltered image available right now.

Your question about the background light positioning should be something you can determine for yourself. You want the background evenly illuminated, and about 3 stops greater than the subject lighting.

Think of it this way. If you meter reads that the subject should be shot at f/8, then your meter should tell you that every section of the background that is visible in the shot is at f/22 (some people might say f/16). You'll also need to keep the subject sufficiently far away from the background that it doesn't light the subject. That's probably about 6-12 feet away.

Joseph - probably the biggest part of your problem is your underexposing your shots. If the background is white, it will affect the metering, and your camera will try to reduce it to middle gray (or at least it will have partial impact, depending on metering modes).

Either go fully manual, or adjust your exposure compensation. Or meter off a gray card. Anything but letting the camera do it itself.

I thought it might be the case because your model look a little dark, but in B&W I couldn't be certain.

this probably wont help you, but i thought i'd share my "po man's studio lighting" with you.

this has been tweaked a little though. my moniter is a poor man's also...