Multidimensional IRT (MIRT) has enough differences from standard IRT that I would get a book on both basic IRT and MIRT. I have a copy of the MIRT book you mention, and think it's pretty good.
For Bayesian IRT, Jean-Paul Fox has done a lot in that area. His articles are always good, so I'm sure his book is good. There's also a Chapman and Hall book, which I think is... okay. I don't especially love it (something about the notation and formulas annoys me, but I can't put my finger on it). But it *does* have some substantial sections on Bayesian statistics before the sections on IRT, if you aren't familiar with Bayesian stuff.
You say you have Likert data -- that's often treated as ordinal, and you will find many different IRT models out there for ordinal data (partial credit, graded response, etc.). But in the case of *actual* Likert scales (e.g., strongly agree ... strongly disgree), you may want to look into unfolding IRT models instead, such as GGUM.
However, a GGUM is a slightly complicated model, and I'm not sure how easy it would be to implement a multidimensional version -- I think I've seen a dissertation or something from years ago, but I'm not 100% sure.
From a practical standpoint, most people tend to use standard ordinal models (e.g., graded response) for "actual" Likert data instead of GGUM, but a case can be made that for certain scales, things like graded response models aren't really appropriate, so you might want to be aware of it.