I don't see the ability to create a bill anywhere via the API. Is there a specific reason this isn't possible? All other major accounting software allow this.
There's a specific reason, although not a specific intention to not support Bills in the API.
Essentially, the public API exposes features of equivalent internal APIs within our systems. Bills is one of the oldest parts of Wave, and currently does not have an internal API in a format that we can use to create a public variant.
At some future date, the Bills feature will be brought in line with the rest of Wave's architecture, and at that time we'll certainly look to expose its API publicly. Unfortunately, I have no guidance when those changes to the underlying systems may take place.
Sorry I can't be more helpful, but hopefully this at least gives you insight into why things are as they are.
I'd like to see the bill available as well.