Well, I'm a BSc in CS, which is very related to SE.
I think it really depends on what you want to do for living. You said you like teaching, but would you be fine teaching hundreds of students in a class on a daily basis? And as well do some research? If so, then you should go for a MSc and a Phd and try to become a professor in an university.
If you are still unsure, probably a good MSc would be a fine option. Big companies usually say that a MSc is considered a bonus, or they even require you to have one (some of Google's jobs require a MSc in CS, for example).
If you can, I would go for the MSc, it also gives you some time to think about and experience what is it like to do research and perhaps even teaching. What you should think about then is what field to do your MSc. I don't really what exactly you study on a SE BSc, so I don't know your base knowledge. However, if you really like the specific SE area, there are MSc programs exactly in SE. Other than that, computing is a large field, you could go for: AI, Computer Graphics, Image Processing (though all of these require some knowledge on math), parallel programming, the list goes on.