I think it would depend on how good your diagnostic skills are. Like others have said, BPII can get confused with other things, including anxiety. It takes one or more good evaluations to sort it out, and we can still be wrong. If the dx is wrong, then that's bad because the patient will continue to "list" it for the rest of their life. And especially if your patient is high functioning or a professional, remember that bipolar anything has a stigma, and be careful about labeling someone with a potentially inaccurate diagnosis. (Imagine if the patient was you, and you had to "report" things to a medical board? You'd want an accurate diagnosis, right?)
The trouble with starting something is that you will have to devote follow up visits to the psych complaint. Are you able to do that? You can't just start the med but never revisit the issue. And bipolar patients tend to be pressured so they talk a lot! Now if they can't get into see a psychiatrist then that's different.
I would have no trouble with a PCP starting a bridge medication as long as it's not a completely messed up benzo prescription like others have mentioned. Starting lithium--I admire you for thinking about it, and it's a possibility for some patients but it depends, and atypicals are easier to work with if you're not experienced. The trouble with a lot of mood stabilizers is that you can't just start them and wait--you have to titrate, or get labs and watch levels, or monitor for side effects. We don't even see our own patients soon enough to do this very well in psych--I'd guess that in primary care, it will be harder.
All that said I admire you for asking and showing interest. Only you can know your own comfort level!