I've been warned by a Sumerologist that the book is idiosyncratic. It does seem to be the only in-print and inexpensive option aimed at amateur scholars.
More mainstream options:
Hayes, John. A Manual of Sumerian Grammar and Texts. A teaching grammar for the beginner. In print, but quite expensive.
Edzard, D.O. Sumerian Grammar. A reference grammar rather than a teaching grammar with exercises and the like. It's really good if you already have some familiarity with linguistics. It's in print and inexpensive.
Thomsen, Marie-Louise. The Sumerian Language: An Introduction to Its History and Grammatical Structure. A reference grammar. Out of print but available on the high seas.
I'm sorry I can't add much more detail as I'm no expert and I'm paraphrasing an off-hand comment I heard around the time the book was published. The short of it is that Bowen & Lewis seem to take grammatical positions at odds with the rest of the field. This doesn't necessarily mean they're wrong. As you are likely aware, the Sumerian language is poorly understood and there's plenty of disagreement among Sumerologists.
More mainstream options:
Hayes, John. A Manual of Sumerian Grammar and Texts. A teaching grammar for the beginner. In print, but quite expensive.
Edzard, D.O. Sumerian Grammar. A reference grammar rather than a teaching grammar with exercises and the like. It's really good if you already have some familiarity with linguistics. It's in print and inexpensive.
Thomsen, Marie-Louise. The Sumerian Language: An Introduction to Its History and Grammatical Structure. A reference grammar. Out of print but available on the high seas.