At that time, Michael Berlyn left the company and he wasn't involved in this project. The only thing he did for their project is to came up with some of the characters they used in, such as Oblivia.[1 53:00 - 1:33:00]
We don't know, when the production started, but what we know is that, they worked in Calico Studios and we also know, who was involved in it. Here's the list of important people and what they're known for. They also have a lot of connections each-other.
- The Director was Tom Burton, Producers we're Claudia Zeitlin Burton and Tom Burton, the Art Director was Ken Leonard (not Ken Macklin) and it was Produced by Calico Entertainment. They are known for making cartoons like Denver, the Last Dinosaur (1988-1989), Widget, the World Watcher (1990-1991) and Mr. Bogus (1991-1993). 
- Besides Calico Entertainment, it was also Produced by Imagination Factory Inc., who also has the connection with Calico Entertainment and that is, they both produced The Adventures of Zorro (1997-1998) and Bad Baby (1997).
- The Writer was Ray De Laurentis. Now this is interesting, because he is known Writer for The Fairly OddParents (2009-2017) and T.U.F.F. Puppy (2010-2015).
- The Storyboard Artists we're Tom Bernardo, Tom Knowles and Ken Laramay. Tom Bernardo and Ken Laramay we're also in the Art Department for Kim Possible (2002-2007). What's more interesting is that, Tom Bernardo was also in the animation department for Anastasia (1997) and a Storyboard Artist for Lion Guard (2016-2019). Tom Knowles was also a Storyboard Artist for Animaniacs (1998) (which he worked for 1 episode), Frekazoid! (1995-1996) and he was also background artist for Charlotte's Web (1973).
- Camera and optical effects we're made by Drew Redford. What's really interesting is that, he was also a Visual effect artist for Sharknado 2: The Second One (2014).
- It was animated by Sei Young Animation. It was an animation studio based in South Korea, known for animating The Super Mario Bros. Super Show!, The Legend of Zelda, and The Adventures of Super Mario Bros. 3. Not to mention, they also animated some anime.
- The Music was made by California Star Productions, who also made music for The Moo Family Holiday Hoe-Down (1992), another Calico Entertainment cartoon.
- The Footages we're used from Archive Film and from NASA. If you want to know, where are clips from, here's the list of their origins: https://atariage.com/forums/blogs/entry/16792-10-footages-origins/
- It was sponsored by Taco Bell.
"The TV pilot had a more southwest, angled feel, and that was okay since the sponsor was Taco Bell (if I recall correctly)" 
-Michael Berlyn, Sega-16's interview
Bubsy - Rob Paulsen (Animaniacs, Pinky and the Brain, The Adventures of Jimmy…)
Arnold, Virgil - Pat Fraley (Krang, Casey Jones, Baxter Stockman, Smurf..)
Terry, Oblivia - Tress MacNeille (Animaniacs, Tiny Toon Adventures…)
Teresa, Ally - B.J. Ward (Scooby-Doo on Zombie Island…)
Buzz - Neil Ross (The Transformers: The Movie , An American Tail…)
Sid - Jim Cummings (Winny the Pooh, Lion King, Tarzan…)
All of the credits:
 https://www.youtube.com/watch?v=jlYW3pof8JI&t (time: 53:00 - 1:33:00)