I think the idea of putting day's dosage in your most controlled prescription bottle is a good one, unless for some reason that made the police more suspicious which I also can imagine. I also think telling them you're bipolar is likely to scare them off as ridiculous as that is.

As it happens I take my sleep medicines and Xanax in prescription bottles when I travel, but only because I don't want to confuse them with the other meds which are in a case. If I were to be stopped and searched for some reason, then let the police check with my doctor and my pharmacist. It would take my time but theirs too if they wanted to bother.