Denatured Ethyl Alcohol Purification
Please note that the following is not meant to be used as an instruction!

According to an article on Detection of Denatonium Benzoate (Bitrex) Remnants in Noncommercial Alcoholic Beverages by Raman Spectroscopy, published in J. Forensic Sci. 2014, 59, 1358-1363 
(DOI), the manufacturers of illegal alcoholic beverages often use sodium hypochlorite ($\ce{NaOCl}$, household bleach) to remove the bitter taste of tax-free technical ethanol. 

In the study above, the authors used legally available legal alcoholic beverages (vodka, cognac, etc.), and denatured/de-denatured them under controlled conditions:


  The separate batch of purchased alcoholic beverages was
  denatured with 20 mg/L of denatonium benzoate, after which 1.33 mL/L sodium hypochlorite was added.


Spectroscopical measurement of the samples thus obtained clearly showed degradation products of the bitterant.

While hypochlorite treatment might be suitable to remove the bitter taste, this doesn't imply that the result is healthy or recommended to consume.