Predictive Single Nucleotide Polymorphisms (SNPs) for Bipolar Disorder
Yes, there have been a variety of studies that do association analysis of variants with bipolar disorder. Here is a recent one that validated 11-30 variants depending on how you count.
However, in these kinds of analyses you should be somewhat cautious as the associations are extremely weak (as they generally are for complex traits in humans):

Eight of the 19 variants that were genome-wide significant (P &lt; 5 × 10−8) in the discovery GWAS were not genome-wide significant in the combined analysis, consistent with small effect sizes and limited power but also with genetic heterogeneity.

The statistics of how you interpret such variants are rather dodgy/uncertain, so I would put very little stock in any particular variant. Maybe if you take the genome-wide significant variants only and added them all up you might start to get a little predictive power.
In terms of other more speculative observations (again from the abstract of that study):

The significant loci contain genes encoding ion channels, neurotransmitter transporters and synaptic components. Pathway analysis revealed nine significantly enriched gene sets, including regulation of insulin secretion and endocannabinoid signaling. Bipolar I disorder is strongly genetically correlated with schizophrenia, driven by psychosis, whereas bipolar II disorder is more strongly correlated with major depressive disorder.

I would suggest reading that paper and finding some further citations from it if you are interested in more detail.