DNP without a BSN?

You should probably check the requirement from each school as they all differ. Some school’s require a BSN or higher prior to starting DNP, but some DNP schools will take ADN with a Bachelor’s degree in discipline (some school make exceptions some don’t, case by case basis) your best bet would be to go with the school that will accept your bachelors in psych and just take the required class, you’ll save time and money. Having your BSN will be helpful and prepare with your DNP because of the BSN theoretical classes, and evidence based research and essay papers, but the DNP program will go over all that, mind you their are a lot of nurses that received their BSN 5 or more years ago so writing research papers will be the same struggle.

Also, does your prospective DNP school require or strongly suggest a minimum amount of psychiatric nursing experience?

No requirements that I know of but I've decided to do my BSN because most hospitals in the area want you to be at least working on it right after or finish it in a specific time of hiring. I feel like I can knock it out within a year (some in my program are concurrent so getting their BSN at the same time as our ASN program and they say the BSN portion isn't that difficult but just a lot of busy work) then I can get experience at the same time.