If you're really interested in WB or IFC long term, I would definitely look into dual degree programs with either an MPP (Harvard Kennedy) or Int'l Relations degree (seems like there are all kinds of different acronyms for them...MALD, MA, MIA, MSFS). Take a look at Johns Hopkins School of Advanced International Study (SAIS) career stats, for example. The school is actually in DC, not in B-more, and a relatively significant percentage go right away to the WB (though not as many IFC...lot of people who goto programs like this have backgrounds like mine, i.e. NGO work). Other schools to consider are Tufts Fletcher, Georgetown School of Foreign Service, and Columbia's School of International and Political Affairs (SIPA). Nearly all of them offer dual degrees with top MBA programs, including Tuck with SAIS, Harvard Kennedy, and Fletcher though sadly Darden only allows you to take dual degrees via UVa constituents...and while I know the other schools I mentioned are of top quality I honestly know nothing about UVa's MPP or MA in IR. They could be great...I've just never heard of them and I'm in a field where these degrees are common.
That said, another thing to think about is how useful these dual degrees really are versus simply the MBA from a ROI perspective (I know....). Talking to people I know who got a dual Columbia MBA/MIA, most said the MIA was largely superflous and didn't really enhance things as much as they had hoped; this was obviously exacerbated by the cost of an extra year of living in NYC without a paycheck and all those other aspects of things that deserve being mentioned.
Also, in the states JD is used almost exclusively in reference to a law school- American law schools offer the JD (Juris Doctorate) to American grads, in addition to LLMs for foreign students. A dual degree in the aforementioned policy/IR fields would be referenced as MBA/MA, or MBA/MPP.
I'd love to help you further than that...but sadly since my area is LatAm and not APAC I can't vouch for the alum networks/career prospects of either school in, say, Tokyo or HK. I however have applied to both programs (and been admitted to Darden) with the intention of going into consulting and then maybe back to IR type work (which the IFC and WB are generally branded under) after some time. I am applying to Booth's IMBA and Wharton/Lauder Spanish track, but find these to be very different from say a Tuck/Sais MBA/MA as they are: A- two years at the same school, not three at two different schools and B- in many ways a good way to focus your network on your area of region within a preset MBA framework.
Sorry for the long post...just passionate about Int'l Relations and how an MBA can help people along in that field. Congrats on the admits, $$$, and consideration for a Jefferson...my UVa undergrad friends STILL talk about people they know who got that as though they were gods on campus.