<p>Some data points which may or may not be helpful:</p>
<p>On double majoring, it may be more common at the LACs which offer engineering. My roommate at Swarthmore double majored in Engineering and Economics. He went on to get a 1-year MS in Engineering Economic Systems at Stanford. In the last graduating class at Swarthmore 7 out of 21 graduating engineers had double majors, mostly in Computer Science but also Economics and Physics.</p>
<p>On how long it would take to get a MS in engineering after a BS - it all depends. The daughter of good friends got her MS in Mechanical Engineering at Penn in one year (or maybe just one semester - I forget) after getting her BS at Penn. She had a lot of extra credits entering and had taken a heavy load (and done very well) in her 4 years for the BS.</p>
<p>On funding for graduate school - many programs in arts and sciences (not sure about Engineering) only admit to their PhD program. If they do have a separate MA or MS program it is definitely subordinate to the PhD program. In math and the sciences the general rule is only to go to a program which gives you full funding - an admission to the program without funding is essentially a soft denial. Math and the sciences not only need TAs and graders, but also professors have research funding and need Research Assistants. Funding for TAs and RAs goes to the the PhD students because they are viewed as more qualified, will be around for many years, and are the real focus of the graduate program. Things are quite different in many social sciences and especially the humanities, but that is less relevant for the OP. </p>
<p>Engineering is quite different in my experience. The MS is quite a common terminal professional degree, and most people go into engineering to practice rather than teach. The PhD is really only required or appropriate to teach and/or do research. The vast majority of engineers are into the more practical side of their discipline.</p>