not that I am disagreeing with you, I'm just honestly interested here. What specifically do you feel the foreign reader would fail to grasp?
The context. With an effort, an American reader can understand what was going through the Pilate's mind, when Ieshua Ga-Notzri dismissed the sanctity of the General Secretary Tiberius' authority - in the presense of the scribe.
But there's just no way anyone who wasn't there can appreciate the countless little details that put things into focus, for an Eastern European.
Off the top of my head -
The main protagonist - Ivan Bezdomny ("Homeless") immediately brings to mind Maxim Gorky ("Bitter"), Demyan Bedny ("Poor"), and a whole bunch of other Leninist pseudo-intellectuals with ridiculous pen-names who (unlike Ivan) never had a transformative experience;
the Patriarch's Ponds (as in: the Russian Orthodox supreme bishop, Patriarch) - the scene of the debate between the hapless "atheists" and Satan - had been renamed the Pioneers' Ponds (as in: the Young Pioneers, a Communist organization for children) long before the book was written; the anachronism would be immediately obvious - and alerting - for any "local";
Nikolay Ivanovich, the guy who gets turned into a flying pig, is, of course, N.I.Bukharin - the original designer of the Soviet propaganda machine, and, eventually, a victim of the monster he helped to create - down to every small detail of appearance and behavior;
the physical similarity of Master with Nikolay Gogol cannot be lost on a Russian reader, but is unlikely to register with an educated foreigner - and Gogol had incinerated the second volume of "Dead Souls" ("manuscripts don't burn");
some conversations Margarita has with various secondary characters are virtually copied from (very popular in Russia of those times) tales of E.T.A. Hoffmann - often recalled in combination with the writings of his big fan Vladimir Solovyev, a significant religious philosopher who could be suggested as a major influence on Bulgakov,
and so on, and so forth.
And these are just superficial factual elements. The cultural and political atmosphere dictates perception of many things mentioned, alluded to, or subtly hinted at in the book.
You don't have to take all or most of it into account, but if all this time-and-place-specific color is drained, we end up with a mere social satire strangely interspersed with Christian apocrypha....
Don't get me wrong: It is still a classic everyone should read. I just think it does not possess the cosmopolitan, extemporal quality of some other great works. Hamlet is above and beyond any particular historical context. Master is incomprehensible for anyone who has no idea what the Soviet Russia was all about.