Dimensions are added automatically by Bambi depending on the levels of the variables in the model. Their names are “{variable_name}_dim” as you correctly point out.
I’m not sure I understand your problem though. Do you have an InferenceData object and you want to modify its dimensions in some way? If that’s the case, it’s more ArviZ/xarray related than Bambi related, but I’m still happy to help if you have an exmaple.