Combining up and down bow over a single note can be done with a macro.

\version "2.24"

% credits: Tina Petzel
% https://lists.gnu.org/archive/html/lilypond-user/2025-11/msg00144.html

updownbow =
  %-\tweak parent-alignment-X #CENTER
  ^\markup \concat {
    \musicglyph #"scripts.upbow"
    \hspace #0.3 % tweak space to your liking
    \musicglyph #"scripts.downbow"
  }

{
  c''1^\upbow
  c''1^\downbow
  c''1^\updownbow
}