Not sure Aeronautical Science would give you enough background to be successful in any engineering masters program. As I understand it, that is typically a pilot-focused major. Taking a few classes to get up to speed may be enough, I would talk to the department at some schools you are interested in. A bare minimum would be two semesters of calculus, differential equations, linear algebra, two semesters of university level physics, thermodynamics, & heat transfer. Then 11-13 more grad courses for the masters degree. (It may end up being less to get the BS degree).
You don't really need a masters degree in engineering unless you are planning to get a PhD or teach.
I'd say this amount of prerequisites is a little low for what you'll actually need these days. Albeit I ended up at an extremely theory-heavy research university as a guy who wants to end up in industry on the flight test side (really feel like the odd man out among my peers sometimes
), here's what I had to take in order to transfer from a 2-year community college into my 4-year Aero Eng program:
3 semesters of Calculus (Intro, Intermediate and Multivariable/Vector Calc).
1 semester of Linear Algebra
1 semester of Differential Equations
2 semesters of Chemistry (Intro & General Chem)
3 semesters of Physics (Mechanics, Electromagnetics and Waves/Sound/Optics... didn't need that fourth semester of Quantum)
1 semester of Engineering Materials Science
1 semester of Engineering Graphics (AutoCAD/Inventor)
(They also wanted Statics and Linear Circuits, but I was able to get in without them and take them at my four year university.)
That's easily 2.5 years of math prereqs alone (it ended up being longer for me because I also needed Precalc/Trig), and 1.5 years of Physics prereqs (which you won't be eligible to take until you start chipping away at the Calculus). If you do end up doing your prereqs at a community college to save money, it's highly advisable you do it at one on the quarter system, because this will
save a lot of time (but throw a lot more material at you in that time).
Since I've been in the four year program, I've taken:
Intro to Aerospace Engineering
Intro to Engineering Graphics (CAD + CNC machine shop projects)
C/C++ Programming
A project based Structural Engineering Materials course
Mechanics I: Statics
Mechanics II: Dynamics
Mechanics III: Vibrations
Solid Mechanics I
Linear Circuits
Mathematical Physics (Partial Differential Equations & Fourier Analysis)
Numerical Analysis (Algorithms like "Runge-Kutta" in MATLAB)
Thermodynamics
Intro to Fluid Mechanics
Advanced Fluid Mechanics
Heat Transfer
Aerodynamics
...and I still have to take Signals & Systems, Linear Control Systems, Aerospace Structures I & II, Finite Element Analysis, Aerospace Propulsion Systems, Spacecraft Guidance, Dynamics & Controls of Aerospace Vehicles, two additional ME/Aero Labs and two quarters of a team-based final project (of which everything else is a prerequisite)... not to mention a bunch of GE stuff and probably a few I'm forgetting.
I know I'm preaching to the choir in a thread full of former Aerospace and ME majors, but I would take a hard look at the above and evaluate whether you think that's feasible. Without all of the above, I wouldn't feel remotely prepared trying to go for a Masters in Aerospace or ME. The difference in workload is going to be tremendous and they're going to assume you know
all the stuff I just listed. Another thing to consider is that ME/Aero is an "impacted" major at a lot of schools, meaning it's very difficult to get into. I get that it's not practical to go for a second B.S. from a financial aid standpoint, but without a prior B.S. in ME or a related field, it could be tough to find a school that would take you.
It's worth pursuing if you're truly passionate about it, but just be forewarned that it's taken me a looooong time (starting from the ground up) and I'm not even out of the woods yet.