From the north side of the Black Sea, you have options to cross into Russia from the Baltic states, Belarus, Ukraine (or even Finland, if you like). Or then you can go through Turkey to Iran (if you can get visa), or around the north side of the Caspian sea, though the Caucasus seems to be a bit of a troubled region... or even by boat across the Caspian Sea to the Stans. That region also seems to have its visa and other permit issues, but many travellers do go through there.
Unless you can pay big time to cross entire China, which would probably cost more than your bike does, your options further east are sort of limited (= go around the north side of China). And you´re probably going to need a carnet to get your bike into Japan.
Vladivostok to Europe I believe has been done on a Burgman 650, so why not with a B-King.....
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