Possible Bachelor's in nuclear engineering......
As a plain-vanilla chalk-on-the-butt everyday engineering professor, my recommendation to you would be to enroll in an engineering program of study that's not so narrow and specialized as nuclear engineering. Nothing wrong with working in that field; it's a good field. However, the name of the degree could be a problem in the future.
Case in Point: Someday you may wish to change career fields entirely, and a whole lotta HR folks will look at your resume and say, "We don't run a nuclear power plant". Result: Your application gets deep-sixed in the file cabinet and you never hear back from anyone.
Instead, You could readily go for a broader degree in mechanical or electrical engineering, meanwhile taking all your general and technical electives in nuclear engineering specialty courses. This approach would work out the same. You'd cover about the same amount of nuclear engineering course material and knowledge that way as you would in the specialty degree.
After your BS degree, you could go for a PE license in your basic area (EE, ME...whatever) and also for a PE license in Nuclear Engineering. An associate of mine has done it that way (EE and Nuclear PEs). [Professionally, I've also been licensed in Nebraska in two separate engineering fields; however, that's another whole story.]
Many BS-engineering grads I've met with highly specialized bachelor's degrees (aerospace, nuclear, petroleum, etc.) have had problems switching fields when their career area dried up and/or when they wanted to move to a different location.
So those are my thoughts for your consideration.
FWIW,