Hey, I'm in the same situation. I have a B.S. in psychology and I'm starting an ASN program in January. I would check the admissions criteria for the program you are interested in applying to. I know the universities here in South Florida (FIU & FAU) both have bridge programs for students who have a bachelor's degree in another field. There are even CRNA Programs that have a bridge component. However, because of the competitive nature of CRNA Programs, I'll get the BSN before applying if I decide to got that route.
Good Luck!
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