Asimov is wanted for bank robbery, murder, and the illegal sale and use of a drug called Red Eye. His first encounter with Spike is when he tries to strangle him to death. His girlfriend and accomplice stops him, not wanting Asimov to add more to his reputation. The two plan to run to Mars and sell their collection of Red Eye in order to live there. Spike knows this and confronts the pair. A dogfight between their ships break out and the pair of bandits head towards a police blockade.

Hakim is a local bounty on Mars. He is wanted for the theft of an illegal data dog from an underground laboratory. He loses track of the dog and chases it all over town. Spike chases Hakim, and chaos ensues. Jet and Spike then use the dog as bait for Hakim to find it. These dogs are worth millions to the right people. Ein, the Welsh Corgi, causes much trouble for Spike and Hakim. Hakim actually ends up turning himself in because of Ein. Spike and Jet can't sell the dog, and thus, the fourth member of the Bebop is born.

Faye Valentine is beautiful but deadly. She has huge, unpaid debts and a bounty has been placed on her head. During a run at a casino, Jet and Spike find the illustrious Faye and take her aboard the Bebop. The debt collectors have something else in mind. A capture then turns into a protection and the pair never cashes in on the reward. The reasons for her debts are explained later in the series. In a bizarre twist, the once hunted bounty eventually becomes a full fledged Bebop member.

Twinkle Marie runs a local environmentalist group called the Space Warriors. They were once a peaceful pact that fought to preserve Ganymede sea life. Once Murdock took over, the Space Warriors turned into a terrorist group. The group would move in and kill anyone offending the Ganymede wildlife. Jet and Spike run after her, with a little help from their friend Faye. Murdock wants to release a virus upon the world, turning everyone into monkeys. After a brawl, Murdock is locked away in Hyper Space.

This bounty comes at a bad time for Spike. He checks it out only to find that Mao has been killed by his comrade-turned-enemy, Vicious. He and Vicious must then meet, because he has been using Julia's name as a code for his Red Eye sales. Mao owns and operates the Red Dragon Syndicate. Both Spike and Vicious used to be under his direction. He was planning on a merger with another syndicate in hopes of finally having some peace. Vicious has plans on taking over the syndicate for his own use.

Not much is known about Giraffe. He has a friend turned rival named Zebra who currently resides with a Harmonica player named Wen. Giraffe is shot and dies in Spike's hands. Before his death, Giraffe gave Spike a rock and tokd him it was the key. They capture Zebra and find out that he has little memory left. He can't talk or move well, and he is still friends with Giraffe. Wen is manipulating him and Zebra is defensless against it. Giraffe wasn't fighting with Zebra, he was actually trying to save him.

Decker is quite the pyro. He is wanted for the illegal use and posession of enhance nitro, a highly explosive chemical. He is pursued with the help of VT, a space trucker that runs into him after he hit and runs one of her friends. Spike and Faye pursue him into an abandoned meteor field and an explosion keeps them in there. Their bounty dies shortly after crashing his rig into the side wall. Lucky for them, Spike and the others can use the enhanced nitro to blast their way to freedom. If only Decker hadn't parished.

The Bebop clan already had the heads up for this easy nab. The three characters were wanted for a set of hijackings. Spike, Jet, and Faye boarded their latest target and waited for the "Duckburgs" to make their move. Spike was ever so graceful, Jet was cool and calm, and Faye just sort of wondered in. The capture went off without a hit. The Bebop crew got their hefty W 1,500,000 and Faye went to go donate it to the local casino. Better than the bank she says.

Early on, Spike meets a young boy named Roco. Roco has a little sister with an eye infection caused by a plant on Venus. In order to cure that infection, Roco decides to steal a priceless plant from a gang he belongs to. Picarro Calvino is the head of the gang, and Spike is the one that connects the two. Spike knows that Roco has good intentions and sets out to get his bounty. Although he hides it, his true intention is to help Roco. Roco finally learns how to be smooth, like water.

Bebop heads to Earth in search of a wanted hacker named Radical Edward. After finding nothing, they hear about an W8,000,000 reward for the capture of a satellite left in the Earth's atmosphere. This satellite has been creating land carvings in South America, and the police have come to the comclusion that it is the result of hackers. Edward tracks down the Bebop and aids them in the capture. Although, the police are very stingy about the bounty. And, the Bebop gets its fourth and final (human) member.

Jet Black's history lies within the gravitational pull of Ganymede. When a bounty drop takes him to his home satellite, he returns to his old girlfriend, Elisa. She, in turn, has a new boyfriend named Rhint. When Elisa goes into debt, she borrows from a loanshark. Unable to pay her debts, Elisa and Rhint are confronted by the loanshark. Rhint kills the man and ends up with a bounty on his head. Jet discovers this and confronts both Elisa and Rhint. Jet gets answers to the mysteries of his past, and Rhint gets justice.

Chessmaster Hex joined the Gateway Corporation at the young age of 30. His intellect and skill led him to develop the Gateway system that is currently in use. However, he found defects and protested that the system should be tested more thoroughly before its activation. The Corporation saw otherwise and activated the system while terminating Hex. Hex vowed revenge, but 50 years later is a long time to wait. He has grown old and senile and has forgotten his traps.

When Faye looks at Ein, she sees her past, but a specific part of her past. She sees Whitney Hagus Matsumoto, a confident man with the talent to woo women. Faye reveals that Whitney helped her with her past, and in turn, became a part of it. A long lost love is soon reunited when Jet rounds up Whitney for a small bounty. Whitney struck a deal with the doctor (who happens to be his uncle) in order to erradicate his huge debts. Now that Faye sees him again, all she wants is the answers to her past.

Domino Walker is a pudgy man with a knack for growing mushrooms. He is wanted for the possession and selling of illegal mushrooms. Since the Bebop clan is currently incapacitated, Ed decides to be a cowgirl, and heads out with her trusty cow-woof-woof, Ein. A man wanting revenge for the death of his brother, along with another female bounty hunter, also try to capture Domino. Ein's quick thinking, and Ed's gelatin limbs save the day. Although no bounty is collected, the Bebop has plenty of food.

The Cowboys' first encounter with these three bandits results in the loss of their mono system, the system that controls the Bebop. Three of their four ships get infected with a virus uploaded via a hook connected to the bounty's ship. Spike gets his ship overhauled and heads out with an old satellite control system. He shuts down his mono system and enables Ed to plant a virus of her own. Spike ends up within the Earth's gravitational pull, and it's Duhan to the rescue.