Well, you "make the jump" by going to nursing school
... There are accelerated BSN programs for people who already have a baccalaureate degree in something else, but it may be quicker and/or cheaper to go through a community college ADN/ASN program, so you may want to look at all
your options before making a decision.
You do realize, though, that there's no "specialty" psychiatric nursing school, right? US nurses are educated as generalists, and your school and the licensure exam will cover all
the areas of nursing -- you will be doing all the personal care, dealing with bodies and bodily fluids (of every
kind), etc., that everyone else does in nursing school. When you graduate and are licensed, you can look for a job in psychiatric nursing, but many psych facilities/units are reluctant to hire new graduates without any prior medical-surgical nursing experience (that varies from facility to facility; some don't mind hiring new grads). In my experience (>20 years in all levels and settings of psychiatric nursing), your BA in psychology will not give you any real "edge" or advantage in job-hunting. Psychology and nursing (even psychiatric nursing) are two entirely separate disciplines.
I'm not saying this because I want to discourage you at all, but I have met many
people over the years who have gotten a BA in psychology and have then gotten the idea that they'd like to be a psychiatric nurse because they're v. disappointed in the employment opportunities available with a BA in psychology, and they see psychiatric nurses doing what looks
to them very much like what they're doing but the nurses are getting paid
a lot more for doing it, so ... However, they have no idea what's really involved in becoming (and being) an RN, and, as they start to find out, typically (in my personal experience) decide it's not for them after all.
That may not be your situation at all, though, and I don't mean to sound suspicious or insulting. Have you discussed your idea with your mother? I'm sure she has a lot of insight and good advice to offer. Best wishes for whatever you decide!