I included the original Japanese lyrics so you can follow the timing easier. You all know how the music goes.

/ Aitai na /
Chasing bounties
/ aenai na /
flying spaceships
/ setsunai na /
fighting bad guys
/ kono kimochi /
making big money

/ Ienai no /
Air of mystery
/ iitai no /
unknown history
/ CHANSU nogashite bakari /
SPAIKU, Jet and Faye and Ed and Ein

/ Datte (datte) Datte (datte) /
Cowboy (cowboy) Bebop (bebop)
/ tsubasa hiroge futari de /
outer space can be so dangerous

/ Sora o /
Rogue AIs
/ marason /
space pirates
/ yume o /
cyber thieves
/ yunison shitai /
even mutant life

/ Hora Catch You Catch You Catch Me Catch Me matte /
But they'll Catch You Catch You Catch Me Catch Me quickly

/ Kocchi o muite /
Handcuffs and pistols
/ suki da to itte /
knockout gas does A-OK

/ Sou Nice To Meet You Good To See You kitto /
Then it's Nice To Meet You Good To See Your Honor

/ Watashi no omoi /
Argue over bounty money
/ anata no haato ni /
lifting off to outer space
/ tonde tonde tonde yuke /
flying flying flying awaaay

/ Ko-i-shi-te-ru! /
Co-W-Boy-Be-Bop!