Let's golf a BIBABOBU decoder
05AB1E, 36 35 33 bytes

Saved 1 byte thanks to Mr.Xcoder
Saved 2 bytes thanks to KevinCruijssen

ć©¡®ì®D…IAO©â'D«‚˜®'U«âJskh2ôJHçJ


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Explanation

ć©¡                                 # extract the head ("B") and split input on it
   ®ì                              # prepend "B" to each
     ®D                            # push 2 copies of "B"
       …IAO©â                      # cartesian product with "IAO"
             'D«                   # append "D" to each
                ‚˜                 # add the leftover "B" to the list
                  ®'U«â            # cartesian product with "IAOU"
                       J           # join each to string
                        sk         # get the index of each word of the input in this list
                          h        # convert each to hex
                           2ôJ     # format as pairs of chars
                              H    # convert to int
                               çJ  # convert from ascii-codes to string