One other thing: generally the site model is not a parameter of interest, but a nuisance parameter (i.e. you don’t care about the site model, except that you need to make sure you don’t pick the wrong site model because it might bias the inference of other parameters, like the tree, that you do care about).
The good news about bModelTest is that it is not so much a model test, as an implementation of model averaging. If you only actually care about the tree then (beyond making sure bModelTest parameters are mixing) you don’t need to look at the output of bModelTest at all. You can just look at the phylogenetic output safe in the knowledge that all possible site models have been averaged over.
Cheers