Thinking about a bachelor's degree in psych

Welcome!

I really don't think getting a bachelor's in psych would help you as an RN. We have folks with that credential working as techs for much less money than a nurse. If you want to learn more about your specialty you can read any number of textbooks on your own for much less money than going to school. If you want more "official" education, I would recommend going for a mental health nurse practitioner--there are Associates to Masters options available now. Just getting a BSN would advance you as an RN, but it wouldn't have the psych specialization which it sounds like you want.
I think you would get more for your money with a masters, and many more options as you advance in your career.

Yes, I'd consider doing the psychiatric nurse practitioner program.

As another poster commented already, a BSN will do a lot more to further your career than an undergrad degree in psych. BA/BS degrees in psych contain very little clinical content, and consist mostly of background material to prepare you to go to grad school in psych. The degree wouldn't do anything (much) to help you be a "better" psych nurse, and it wouldn't benefit you professionally.

I would have to agree...a bachelor's in psych is not the way to go.