Do Bardock and King Vegeta make appearances in Otherworld? This is a two part question:


If Bardock and King Vegeta are dead, do they ever make appearances in HFIL or Upper World? One would think that either Goku or Vegeta would want to pay their fathers a visit. 
Do Goku or Vegeta ever mention their fathers once during the entire anime?


I don't recall any of this. Feel free to include the manga if anyone has that much knowledge on the matter.
Anime and GT series make a lot of confusion with its fillers, but in the manga, Piccolo explains water-clear to Vegeta.

Evil souls are cleaned, their memories wiped, and then reincarnated.

Both King Vegeta and Bardock, although heroic, are clearly evil, so they are impossible to visit.

Goku never shows interest for knowing about his father. He was raised by humans, and he consider his adoptive grandfather as his true ancestor.

Please, also notice that HFIL is an invention of the American dub, which you should avoid if you are really interested in Dragonball canon. Where Goku goes is called the Other World, and what is written on the otherworld's demons' shirts is "HELL".