Okay, so this is a mediocre answer because I don't own the book nor have I read it, so I cannot assess it clearly. I am pretty curious about it so I may try to pick up a copy. However, doing a really quick literature search, the book Computational River Dynamics by CRC Press seems like it has all the ingredients to be a good introduction based on the description and table of contents. It also appears to be fairly well cited.
It covers the governing equations and submodels that are needed -- sediment transport, simplified 1D/2D models as well as the full 3D models, etc.. It also covers numerical methods and a variety of formulations that can be used.
It seems targeted as a reference book, but says it has worked examples. So it may be less narrative and more formulaic, but I cannot determine that without the book. However, it will almost certainly have references in it that point to good review articles and papers with details on all of the methods it covers.