Bundism wasn't about opposing Zionism
Bundism wasn't created to oppose Zionism; it was created as a solution to the very same crushing oppression faced by European Jews of the time that Zionism was created to solve. The Bundists' opposition to Zionism was secondary to their particular solution to the problems they faced: crushing poverty, constant pogroms, and a general lack of prospects for education or for improving their situation. The oppression they faced was all-encompassing; it was so bad that it resulted in the Holocaust, then continued afterward. Holocaust survivors spent years in the displaced persons camps that dotted Europe, often suffering additional antisemitism, and Ashkenazi Jews in the Eastern Bloc faced a series of horrific repressions: the Slansky trial, the so-called “doctors' plot”, the slaughter of Jewish antifascists who had helped the Soviets during the war and were trying to rebuild the Jewish people after the Holocaust, the campaign against “rootless cosmopolitans”, and more.
Prior to the Holocaust the Bundists, looking at the horrible situation faced by Ashkenazim in the Russian Empire, saw their best hopes in revolutionary Marxism. A group of Russian Jewish Marxists created the Bund a little before the Social Democratic Labor Party of Russia, out of the belief that something like it would be created. Soon they became part of a movement that included the future Bolsheviks and Mensheviks, Trotsky, and others. Though they saw themselves as part of a much larger movement and were, they specifically were created to organize the Jewish proletariat. They knew that they had specific needs that set them apart from other workers, such as fighting antisemitism (which generally came from their fellow workers) but also acquiring autonomy for the Jewish nation over Jewish affairs.
And they did view the Jews as a nation, like every Jew did back then, save some assimilated German Jews. Bundist intellectuals developed a version of a philosophy known as “national personal autonomy” where every nation had a degree of autonomy over its personal affairs, and everyone was free to join whichever nation they wanted. Lenin's concept of self-determination, which forms the basis of the current UN concept, was created in opposition to the Bundist philosophy. The Bolsheviks smeared Bundists as “Zionists with seasickness,” and many leftists today share the sentiment that it is “Zionist” to view the Jews as a nation or to speak of specifically Jewish needs. A creeping number of things inherent to both secular and religious expressions of Judaism have come to be seen as “Zionist” today, in part owing to Soviet propaganda.
The Bund, though, saw themselves as practical and the Zionists as utopians with plans that would never work out. The Bund believed the imperial powers would never allow the Jews a state in Palestine, and that Zionism was therefore not based on materialism; it lacked historical possibility. They wanted to create a better world for Jews, to attain self-determination, and to build a culture worth being proud of. Their concept of doikayt meant they believed they could do it right there in Russia.
Two key differences between the Bund and the Bolsheviks were that the Bund desired Jewish autonomy and the Bund rejected democratic centralism, Lenin's authoritarian philosophy. In this second bit, they formed a majority together with the group that would come to be known as the Mensheviks. Hence at an early meeting of the RSDLP, the Bund asked for autonomy over Jewish affairs, reasoning that they already had a mass movement unlike the other factions, and their request was rejected. Their delegates walked out because of this, and control over the party newspaper was handed to the group that would come to be known as the Bolsheviks.
Of course, in the end, most of the Bundist leadership ended up kissing Lenin's ring as his power increased, becoming part of the mainstream Bolshevik establishment. They were, in effect, given an ultimatum, and most of them chose to become part of the new ruling class, often harshly oppressing the very Jewish workers who they had been organizing into the Bund. Then, of course, many were later purged by Stalin due to his suspicion of Jewish international ties. After Stalin had gotten all the use he needed out of Jewish antifascists during World War II, labeling a Jew a Bundist became synonymous with naming them a traitor or a spy for the international conspiracy of “rootless cosmopolitans.”
In Poland, though, the Bund kept going after Soviet liquidation, continuing to reject the authoritarian philosophy of Lenin, and eventually fought in the Warsaw Ghetto Uprising alongside both Bolsheviks and Zionists. The Holocaust destroyed Jewish life in Poland, though, and the Bund along with it. The International Bund, formed to support the Eastern European Bund and spread Bundist ideas, helped create a lot of institutions that continue to exist today, but itself ceased to exist in the early 2000s.
Any attempt at “Neo-Bundism” can't ignore the real purpose of the Bund. It was never about Zionism. As much as the Bundists viewed Zionism as a threat that was stealing workers away for some utopian pipe dream, and as much as the Polish and International Bunds reacted with horror at the news of Zionist dispossession of Palestinian Arabs after World War I, the Bund's main emphasis was always on Jews, which angered their enemies on the left to no end. The Bundists were concerned with creating a more just society for everyone, but also with creating a just society for Jews, including by fighting the antisemitism among their goyishe comrades. And this latter bit is something “Neo-Bundists” have to start doing more of.
There was, of course, an option C that many oppressed Ashkenazim ended up taking, which was to go move to one of the many genocidal, colonizing powers in the Americas. Though initially facing near-universal rejection and contempt upon arriving, and continuing to face dehumanization and persecutions for decades, they were slowly assimilated into whiteness, which improved their prospects drastically. This option was not better than Zionism. It was, however, the only option available to many. For others, Zionism was the only option available. Most had little choice of where they ended up.