Linnaean classification has been abandoned as unfit for purpose. People tried to patch it up with sub-orders, infra-orders, super-genera and hacks like that but it became unworkable.
These days, biologists use cladistic taxonomy: organisms are categorized based on shared derived characteristics that can be traced to a group's most recent common ancestor and are not present in more distant ancestors.
We, and bonobos, are apes because our most recent common ancestor had the characteristics of an ape. We, and bonobos, are also monkeys because our most recent common ancestor with monkeys would have been classified as a monkey.
You recoil from that? But you have absolutely no problems with admitting that we're placental mammals (like cats, dogs, etc). Or that we're mammals (which includes the non-placental mammals like kangaroos and the duck-billed platypus). We're also vertebrates (which includes birds, reptiles, amphibians, mammals and fish). You'll probably also admit that we're animals (although you might need to be pushed into that one by first admitting that we're not plants or fungi).
Cladistic taxonomy has some interesting outcomes. Birds are classed as dinosaurs. Which is really cool. Mankind really did walk with dinosaurs, and still does. Just not the big ones the creationists would have you believe.
Cladistic taxonomy is not without problems. Technically we're also fish. We're derived from that branch of fish that moved onto land. In that sense, birds, amphibians, and reptiles are also fish. Biologists tend to avoid mentioning that, but it's how the system works. A clade starts at one point on the tree of life and encompasses all of its descendants. Those of us who aren't biologists tend to use "fish" in a non-cladistic way because it's more useful in everyday usage.
So, yes, bonobos are monkeys. Unlike most monkeys, they're also apes. As are we.
For more details, see This video by Aron Ra (contains language that some people might consider NSFW).