I am curious: what schools are you considering? MIT and Caltech are probably the most prestigious, but there are several others that are very good.
Yes, you should at least continue your studies to a Master's Degree, better to get a Ph.D.. Graduate studies is when you actually specialize in a particular aspect of research. And a Ph. D. usually involves quite a lot of industry collaboration; in other words, your Ph. D. research will help your networking and bring you into contact with many of the people in a position to offer jobs. If you stop your studies at a Bachelor's degree, you will have been exposed to a few basics of the aerospace sciences but, honestly, you won't be very good at anyone of them in particular.
Also, you might consider an alternate approach into the Aerospace industry: electrical or mechanical engineering. It seems that many aerospace companies hire specialists in fields OTHER THAN Aerospace Engineering (for example, mechanical engineers for the landing gear and fluids, electrical engineers for sensors and controls). I rarely see posting for Aerospace Engineers. And especially with the latest cut-backs and shut-downs at NASA, an Aerospace Engineering degree might not be as practical as one in, say, electrical engineering.
My advice:
Check out the jobs boards such as monster.com, hotjobs.com, and careerbuilder.com. Pretend you are seeking a job NOW. After a few days of surfing these sites, you'll get a pretty good idea what employers are seeking.
Also, if you get chance, get some exposure to CATIA. It seems to be pretty popular in the aerospace industry. You might also want to get some exposure to the Satellite Toolkit (stk.com); in fact, they send out free CDs to student and industry professionals.
Here's another small tip, a website I find very handy:
Rocketscientists
It lists several resources intended for students.
Whew! That's about it. I guess I should mention that if you ever have to choose between employment with Lockheed Martin and Boeing, go with LM. They seem to have a better environment and more devotion among employees. I have heard of Lockheed Martin men, but I have never heard of a Boeing man (I guess Boeing is more about money and treating people as expendable company assets).
Regards,
Duncan