T thinks I have bipolar but psychiatrist isn't so sure?

I've been seeing my T since November of 2015. I feel safe in her office and tell her most everything. I started seeing a psychiatrist in February, and he diagnosed me with depression and generalized anxiety and gave me scrips for both.
Now my T has never said to me what she thinks I may have (possibly because she's a doctoral student so maybe she feels unqualified) but I know from my psychiatrist (who has access to my T's notes) that my T thinks I have bipolar.

My psychiatrist, who I have only ever had two appointments with, says he thinks the bipolar diagnosis is "soft." I know he has a medical degree while my T is still working on her PhD. But wouldn't my T know more than him? She really knows me, she really listens to me. The only questions my psychiatrist has ever asked me about how I feel are if I feel suicidal and how I'm feeling in that moment.

You'll need to try the suggested Meds and see how you feel.
When a person suffers bipolar, some Meds are not used.
The T knows you better, but the Pdoc should recognize what Meds are appropriate.

Depends on your T. My first T was interesting... I had been seeing her for a while before I started seeing a pdoc. (She was the one who convinced me to see a pdoc and try medication.) Despite everything I told her, she literally said to me, "Bipolar?! I don't believe you're depressed. I don't think you've ever experienced depression before", even though I've had on-and-off suicidal thoughts since age 11. And this was a T who allegedly had "30 years of experience".

So, T's aren't perfect. Maybe your T is right and you are BP. Or, maybe your pdoc is right and you're *not* BP. Either way, an antidepressant will probably tell you if you're BP or not. Antidepressants usually worsen depression, cause a mixed state, or cause hypo/mania in BP people.

Do you have any idea on what your therapist might base her suspicion?

Do you ever feel "on fire"? Are you having problems maintaining a regular/consistent sleep rhythm? Ever feel like you can do things or know things (much) better than others and feel like being on some "special mission" to prove it? Ever get depressed because you feel you are losing control or you meet (lots of) opposition? Ever having lots of creative ideas?

Yes to all of those things. Obviously I am not a trained T or Pdoc or anything but from what I've researched about bipolar I am inclined to agree with my T. She knows me best and listens to everything I tell her and that's what she is basing her suspicion on. I don't tell those things to my Pdoc (because he doesn't ask) so he doesn't really know how I am feeling regularly.

I wouldn't know if that's possible, but could you maybe have appointments with your psychiatrist (only) when very depressed or hypomanic? So he might see for himself? Is always something which might benefit you, so they can monitor, not just for a diagnosis.

Maybe you could ask for a second opinion?

Why does it matter? That sounds SO crass, but that's exactly what my therapist and psychiatrist would say. There's so much overlapping all over the place that diagnosing is super hard.. and doesn't really accomplish anything more than as a reference for insurance companies.

Your therapist and psych should be focusing on symptoms and relieving them - not naming them or putting you in a box. We all just don't fit in one specific diagnosis.