I don't know if this makes sense, but I'm trying to make my logo stand alone, that is without any background. I would like the PY logo to float on top of what ever I use it on, such as business cards, stationary, or whatever. I don't want the white square behind the logo to appear. Just the logo. I would also like this in JPG or BMP if at all possible. I hope this makes sense...

Bmp and jpeg can't have any alpha channel -meaning it can't have a transparent background in those formats.
Png is for such purposes.

At the document's preferencies panel -entered by Shift+Ctrl+D- no alpha was given to the background.
Now it is corrected.
By the way it could have a more professional look without that 3D-like effect.

Also, just to add a little more info to Lazur's good advice, and in case you aren't already aware, your image, as drawn in Inkscape, does have a transparent background by default. Inkscape has simply chosen to have a white background to make it easy to draw on, by default, however, if you don't like it, you can draw your own checkerboard background (like many software pkgs have, GIMP for example), and use it in lieu of the default (basically you change your default template). The white background is added when you save as a jpg, eps, and some other extensions, etc. Exporting as Png, as Lazur said, does allow you to retain the transparency. For learning about changing your default to a checkerboard (if even interested), you might want to search the forums here, because there are a couple of good threads on it, and better said than I can relay.