I don't have experience dating someone with bipolar disorder, but I've had a few friends who are bipolar.
Keep your relationship honest with minimal drama (if it resembles any couple on tv, try couple's counseling). Be polite and assertive with each other about your desires or preferences to prevent unnecessary fights/arguments/emotional tension. Learn basic mediation techniques, like using "I" statements when phrasing a concern or cause of unhappiness, and use them to resolve conflicts without hurtful arguing. This is useful in any healthy relationship.
Learn as much as you can about bi-polar disorder in general, then learn the specific patterns and symptoms your partner experiences. This will help you be aware of any problems and react appropriately in an understanding and supportive manner. Don't, however, showcase that you are recording her behavior, as it can be perceived as controlling and condescending.
Encourage regular appointments with her psychiatrist/counselor and be supportive (but don't nag) with whatever exercises or suggestions are prescribed. This may include charting her energy level or keeping a journal.
Have a list of contacts, like her doctors, family members, helplines, and whatever resources you may need should an emergency arise. Ask her to help with the list because
(1) she may have some useful suggestions and
(2) you don't want her to find it (if she doesn't know about it) and feel you are planning to gang up on her. Keep the list handy at all times.
Ask her if she'd mind if you met with her doctor/regular counselor. Have a private appointment to voice your concerns and get a professional's answer to your question. Let him/her know what you plan to do (like if you plan on following any of my suggestions) and ask for suggestions and recommendations to improve them. This person is the most reliable resource for answering your question, despite all the well-meaning answers, including mine, on the internet.
Lastly, if you have children, be aware of their emotional patterns for the same reasons.