Does bleach turn a substance white or colorless?
First, let's think about what makes a substance coloured: a substance will appear to be coloured if it absorbs light in the visible spectrum. Beta carotene:  

absorbs blue/green light (400–500 nm), so it looks red-orange when white light is shined on it as the blue/green light is subtracted from the white and what remains is what reaches our eyes. The details aren't dreadfully important, but you'll notice that the molecule has a lot of conjugated double bonds. This is what allows the molecule to absorb visible light and this conjugation is what produces the colour in many things that might stain clothing or the like. The size of this conjugated system affects how it absorbs light. In general, the more conjugation, the more absorption occurs and at longer wavelengths (towards red).

Substances used as bleaches tend to be oxidizing agents. Again, the details aren't too important, but one thing oxidation can do to these conjugated molecules is break them apart or convert double bonds to other functionalities. By disrupting the conjugated system, one changes the absorption properties of the molecule. Breaking the molecule apart or removing double bonds shrinks the extent of conjugation, reducing absorption and shifting it to shorter wavelengths. If the wavelength is short enough, the absorption is the in the UV range, which is invisible to the human eye, making it colourless.

Now, to your questions:


  From what I understand, bleach works to weaken the ability of a substance to absorb light.


This is as described above.


  Thus this seems to be "whitening" i.e. reflecting all light.


Reflective/scattering properties are distinct from absorption. e.g. if I add bleach to an aqueous solution of a dye, it may go from a coloured clear solution to a colourless clear solution, but if I bleach a shirt stained with a dye, the shirt doesn't become transparent—the reflective properties are determined by the fabric, not the dye. Bleach simply changes the structure and thus, absorption of the dye, it doesn't render them reflective.


  So is 'colorless' a misnomer when used to describe bleach?


Colourless is the correct term to describe the effects of bleach—it makes coloured substances colourless.


  Also, to double check when you bleach something, is it still there? Only that it is now white??


The coloured molecules undergo a chemical change so they aren't the same substances with which you started. Whether the products of the reaction are still there depends on what they are. It may very well be that the oxidation products of a dye are more soluble and easier to remove when you wash a piece of clothing. The bleaching itself implies a chemical reaction that alters the absorption of coloured substances, not their removal.