Maybe it'd be something the Austro-Hungarians play with in the empire, as a means of putting a face on Jewish issues, making them easier to use and manipulate, the way the Croats, Hungarians, etc all had their own organizations?
Alternately, during WWI, the Bund and the Germans come to an understanding, and with other Ethnic/nationalist organisations, work against the Russians, or more accurately, in their own self-interest, with the Bund organizing community affairs like running civil defense programs in Jewish settlements, and arranging for interpreters for German units on occupation duty (indeed, perhaps a number of volunteer Pale-Jewish infantry units, like other "Free" Ethnic units are raised by the Germans to fight on the eastern front, to fight Russian oppression.)
Given some politicking in the US, and a generally smarter PR team in the US (which, frankly would be easier, now that they can get American Jewery, the Poles, etc on side,) and it'd be possible for the Central Powers to just outlast the Entante, (save Japan) as British money has to run out sooner or later.
Post war, the Bunds keep doing the first two on a more official basis in Poland, Belarus and the Ukraine, and transition back to being a more conventionally socialist group like they were before the war. Of course, they just happen to have some nice stocks of military surplus equipment, and the training and command and control structure to use it effectively as well (as they'd be in that weird little cross section between a trade union, political party, mutual aid society, and an armed militia.) All of which makes them very valuable allies for any faction in a less than stable new country, and does ensure that their demands do get heard.