My dentist polished my teeth after the bleaching. Is that normal procedure?

There is nothing wrong with polishing after bleaching.  Your dentist may have a polishing paste that contains oils that could interfere with bleaching.  Any polishing paste that is not free of oils should be delayed until after the bleach process.  In my office we often polish if needed with oil free pumice before applying peroxide and sometimes polish with a teeth hardening mineral paste after the bleaching treatment is completed.

There are some stains which are resistant to bleaching but can be removed with polishing.  The usual chronology is to have your teeth cleaned and polished before bleaching is done - this maximizes the bleaching effect.  That said, there is nothing wrong with polishing after the bleaching is completed.