From my VHS recordings, here are the bumpers and promos (and occasional commercial) that aired during Inuyasha on Adult Swim in the Winter/Spring of 2003.

Included here:
1. The "Parents Strongly Cautioned" bumper (the last part of it, didn't catch the whole speech). By this point, they had replaced the robotic voice (as seen in the last upload) with a human voice.
2. The Adult Swim "Inuyasha intro" (2nd version). This is the version that aired in 2003 when Inuyasha was airing weeknights (as Adult Swim had transitioned to weeknights at this point). This started in January 2003.
3. Adult Swim "Instruction Manual" bumper ("hole in chest" version). From January 2003 to May 2003, Adult Swim briefly used these style bumpers, usually focused on "teaching martial arts".
4. Adult Swim "Instruction Manual" bumper ("falling apart" version).
5. Adult Swim "Instruction Manual" bumper ("flipping through the manual" version)
6. Adult Swim "Instruction Manual" bumper ("Kung-Fu doesn't work on giant robots" version)
7. Inuyasha end credits (the second version of the end credits, from the second half of Season 1). If you were like me in 2003, this was the last song you would hear before heading to bed.
8. Adult Swim "Instruction Manual" bumper ("head popping" version). This is the "up next" bumper, showing "Cowboy Bebop" was next.

Stay tuned, more to come!