First off, I like your username.
Secondly, when using clothes like this, watch out for bunched up folds of skin like on her back here. That's the first thing that stood out to me.
Third, if you wanna shoot in camera closer to the second image, you're gonna need a large light source, set far enough away to throw light evenly on both the model and the wall she's leaning up against.
As an example, here's an unedited photo (other than removing the dust spots from a dirty sensor
Here the wall is approaching white all over, but I wasn't able to pull it back far enough in my small apartment for it to spread completely evenly (so I adjusted the curves slightly after the fact to make the whole thing white). Also, in this case I wasn't using a large, soft light source, but a small, harsh one.
Also, make sure your white balance is set properly. Looks like (and correct me if I'm wrong) you were using tungsten lights and a daylight white balance. Having your white balance set for the lighting you're using will help to make your white background look, well, white.
Or... You could just give your shot more exposure, but that'd make your model brighter, too. In this case, that would help too, as it looks to me that your original shot is underexposed slightly.
And finally... keep shooting!