This will vary from school to school. There is no 'uniform
At my own institution, there are two options for the ASN-prepared nurse who has an undergraduate degree in another area.
Path 1: Pursue a BSN (12 months), then a specialty MSN (2 years fulltime, 3 years parttime).
Pathway 2: Pursue a generalist MSN (clinical nurse leader (18 months). Then pursue a post-masters NP program (12 months fulltime or 24 months parttime).
I know of two other schools in Virginia that will enroll the ASN-parepared RN with a BS/BA in another subject directly into the specialty MSN programs after completing 2 classes in the RN-BSN prorgam. No BSN degree is conferred though.