As far as the meaning is concerned, Bill was both Zoot Horn Rollo (who was even thinner and more pale than the rest of the group, which is saying a lot) and the name of a goldfish Beefheart had as a kid (hence the "Goldfish in the bowl lay upside down bloatin'" line). The woman in the song seems to be the angel of death but it's not clear.
If you're curious about the song meanings, I recommend reading Mike Barnes's Beefheart book. Really well-written and considered the definitive biography. Here's an excerpt from the TMR chapter (in 2 parts), which discusses song meanings: http://www.furious.com/perfect/beefheart/troutmaskreplica3.html