akcampbell 1 points
When you say "transfer to a neuroscience program" I gather you don't actually mean that you are "transferring" but rather that you are "applying to grad school." Am I correct? "Transferring" is what it's called when you move to a different school *before* you receive a degree. If you've received a degree and then go to a different school - the most common reason being grad school - then you have applied to that school and been accepted, you have not "transferred."
That being said, whether or not your Biology B.S. from Paul Smith would be good enough to get into a given neuroscience program likely depends on where you want to go for graduate school. From what I've gathered in some of the previous threads in this subreddit, your letters of recommendation and undergrad research count very heavily, as do a good G.P.A. (3.7+) and good GRE scores. Your undergrad institution affects what research is available for you to do, and what scientists you will come into contact with as your professors. I'm still an undergrad at the moment, so I can't speak from experience on that.
But if your question is about whether a regionally accredited school's B.S. degree would be accepted at all by a certain graduate school, then that is a question for that school's academic advisors or Paul Smith's academic advisors.