I think perhaps I was misunderstanding. I thought you had applied your Likert scale variable questions as covariates within the HB estimation routine, meaning that the alpha file would contain successive estimates across iterations of the effect of the covariates (as regression weights) upon the part-worth utilities.
But, maybe you did not include these Likert questions during your HB estimation, but only need to use them as predictors of part-worth utilities estimated separately using plain vanilla HB (without covariates)?
There are many ways to do that, but I would think you'd use the zero-centered diffs (normalized) utilities that our HB software outputs. You'd read those along with your Likert scale questions into a software package like SPSS, R, SAS, etc. Then, you'd do statistical tests on whether the Likert scale questions were significant predictors of respondents' preferences. One simple test flows from regression, for example.