So basically I’ve come up with a story that I believe could be an interesting animated series, but I’m not in the stages where I’m ready to try and pitch it or anything. How should I approach writing out the entirety of the story if I feel it should be a show but I’m not necessarily ready to create a pitch bible? I'm more in the stages of developing the world and characters and storylines. Do you think I should approach it as if I’m writing each episode or maybe a comic book, novel, script etc.?
Write the first episode as a pilot – the first episode can stand as a 1-off that represents the tone of the show. Your priority is to finish this episode and get it produced.
The pilot is not an origins story, or a slow build up where we meet these characters and learn about their backstories. The pilot needs to be almost in medias res, with your character(s) hinting at their entire arc during an encapsulated crisis. Borrowing terms from a novel or typical screenplay, this episode is your character's call to action in the larger context of the series. But here it also needs to function as a stand-alone story with a satisfying conclusion. We see these characters shine and show who they will become by the end of the series.
Connect the first 4 to 6 episodes with the first major character arcs (as opposed to the big plot). These will be your test series – should you be so lucky to get the project greenlit. There are no rules for the length of an animated series. TV "seasons" use to be ~24 episodes, but distribution is meaningless with streaming and pay-per-view.
Include a variety of "plots", A and B, within these first episodes. Avoid the "big conspiracy" plot arc, and instead focus on settling these characters into their new roles, making mistakes, showing all the flaws you didn't have time for in the pilot.
By the end of this test season, you have established a formula for however long you want to continue. Ideas after this are really just ideas. Your attention needs to be on the pilot and then the test series. In the real world, the show's producers will be finding elements that work and things they want changed. No screenplay has ever been produced as originally written.