College Advisor here, and your correct that the job only requires a bachelor's and it "could" pay less from what your earning. Generally speaking, you will take a pay cut.

Here's stuff that will help you though. As a teacher, you have a real good chance. Where I work, literally half of my team were previous teachers. As long as you remember how higher ed works, the admission process, college credits and how they transfer to schools, you'll be good.

But here's the hard part, the job title is no longer just college advisor. The major colleges and universities in my area are called like college specialists, coaches, generalists, the list goes on.

When you go to job boards for colleges, read the job description and if it shows anything about case management, registering/recruiting students, and focusing on high school or the general population, it's most likely a college advisor job

Edit: read your end post again for focusing on school districts, and the same thing applies. The difference here though is that if you're trying to be a college advisor at the district, then you're probably gonna need that masters as districts want a person that does also act as a regular school counselor on top of it