GSW Homomorphic Encryption
However, usually in lattice based cryptography a balanced
  representation is used [...]


Is this true? I'd be interested in seeing some instances in the literature (or implementations) which actually use this representation. In my experience, the literature (such as the paper you linked) assume the ordinary representation of $\mathbb{Z}_q$.

I don't see a practical benefit to using the balanced representation. Random numbers are indeed sampled from a truncated discrete Gaussian centered around 0, and a negative number can easily be added to the value in $\mathbb{Z}_q$. Sometimes this result may be negative, so a $\mod q$ operation needs to be done. But this operation is necessary for whichever representation you use. In the balanced representation, if you add a positive error to $(q-1)/2$ you will need a $\mod q$ operation as well to keep the result in $\mathbb{Z}_q$.

To answer your question, the Bitdecompose procedure can be done by simply adding $\lceil-q/2\rceil$ to $a$ first, which shifts the representation back to normal. Then Bitdecompose is nearly free in practice.