This is a question that we will also never have an answer to. At the beginning of the Cowboy Bebop series, Spike and Jet have already met one another and are working together as partners. Though the rest of the crew had yet to join at that point, they were at least bounty hunters on the same team. We do not get to see how they first met each other and agreed to work together, and it is not hinted at by the characters either. That said, there is a bit of rivalry and differing personalities for the two of them so there is the chance that they had a competitive or possibly forced partnership at the beginning of their relationship. Some fans have even suggested that it could be similar to the relationship between Spike and Andy during the Teddy Bomber episode where the two are competing against one another as rival bounty hunters. I could see a similar bounty mission like this but less violent and with Spike and Jet eventually having to work together.