Good question! So typically the difference between a BS and a BA would be the number of math and science classes that your degree requires. For example, at a lot of universities, you have to at least take introductory biology, chemistry, and physics in order to earn a BS. Your academic adviser at your university should be able to show you the different degree plans so that you can see the additional classes you would need to take for the BS. You can likely find that online as well, but I always found it useful to talk with someone about it in person when I was degree planning.
Whether you should go for the BS or BA would depend on your future plans and how science-oriented they are. For example, if you know that you'd like to eventually pursue a graduate degree in neuroscience in psychology or another field where you would be conducting research, it would be in your best interest to earn a BS to prepare you and make you competitive in your graduate school applications. If you're thinking of going more into a clinical or counseling psychology graduate program that focuses on practice, then you may not need the BS - you can look at specific graduate program websites to see the prerequisites that they require.
I usually assume that those majoring in psychology are planning on additional schooling beyond their bachelor's degree because most things that people tend to want to pursue with psychology require an advanced degree. However, if you are thinking about jobs that do not require an advanced degree, then I would still consider how much science/math knowledge you would need in that job.
Hope you found this useful!