yes a person can have both bipolar and dissociation problems. put simply even non mental disordered people dissociate. the defining line is severity. dissociation moves from the normal levels into the disordered levels (the list of dissociative disorders we have here in america is listed with in the link at the bottom of my post other locations outside of america may have other diagnostics and dissociative disorders)

here in america depression now includes dissociative problems, bipolar is a type of depression therefore your treatment providers might have already considered the dissociative criteria of the problem cant be better explained by another mental disorder and decided your problems are better explained by bipolar disorder.

short version america is moving away from the multi axial (many mental disorders ....diagnostic process) so now mental disorders include the diagnostic criteria that the problems can not be better explained by another mental disorder.

what that means is many people who have more than one mental disorder label are being re labeled as one or another disorder rather than having many mental disorder labels stuck on them.

my suggestion contact your treatment providers, they will explain to you why your problems are called bipolar instead of dissociation disordered.