Bittersweet lolita is a relatively new sub-style. Some people claim it is not a style at all and should simply be labeled under sweet, others feel it's different enough to deserve a name of it's own. But honestly, most sub-styles have fairly blurry lines. Is Country or Hime all that different from plain ol' Sweet lolita?
The biggest gripe I've heard is "It's just a black colorway of a sweet print". I can understand this sentiment. To me, in order for an outfit to be bittersweet, there's got to be a little more "bitter" to it than just a black colorway. I would define Bittersweet as having strong contrasts of pastels and black, in relatively equal proportion, occasionally intermixed with gothic themes such as skulls, bats, eyeballs, etc.
To illustrate, here I have two sets I made on Polyvore, involving the same AP print Toy Parade in a black colorway, as well as some example co-ords I've found.
This is what I consider Bittersweet. It's coordinated primarily with black accessories, and there's an extra "punky" touch with some cute Doc Martens. The other two examples also have a darker edge to them than most Sweet lolita- heavier make-up, funky hair, big boots, etc. You can also use a non-black colorway if there's elements in it that let you coordinate it with black (one the reasons I love Fantastic Dolly so much).
The second set is straight-up Sweet lolita. Simply a black colorway with traditionally sweet accessories. The overall feel of the two examples is still Sweet, and lack a "bitter" twist to them.
As I mentioned earlier, I don't think bittersweet even has to include a black colorway. Or a print at all (for a non print example, there this post I made about adding Bittersweet to a Gothic wardrobe last year).
Here are some examples I've worn.
Basically, if your coord floats somewhere in a candy-coated netherworld between Sweet and Gothic, it might be called Bittersweet.