The best replacement for bullnose is quarter round.

The best alternatives to bullnose are rated as following:
★★★★★  quarter round
★★★★  eased edge
★★★  surface bullnose
★★★  schluter
★★★  half bullnose
★★  ogee
★  square edge
★  double bullnose
★  bevel
★  ball nose
★  beveled edge
  fullnose

Your alternative for bullnose is not listed? Suggest!
Speaking about bullnose, one probably shouldn't forget about edge.

Other search terms related to bullnose and their ratings are:
★★★★★ edge
★★★★ mosaic tile
You have in mind a companion for bullnose and it is not yet here? Propose!



Google Trends

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bullnose
quarter round
eased edge