I am using a custom style to address this problem. For a MWE, let's use a test.bib file like the one PLK prepared:
@COLLECTION{yanagida_zengaku_sosho_1975,
LANGID = {japanese},
EDITOR = {柳田聖山},
editor_romanised = {Yanagida, Seizan},
TITLE = {禪學叢書},
TITLE_romanised = {Zengaku sōsho},
TITLE_translated_english = {Collected Materials for the Study of Zen},
LOCATION = {京都},
LOCATION_romanised = {Kyōto},
LOCATION_translated_english = {Kyoto},
PUBLISHER = {中文出版社},
PUBLISHER_romanised = {Chūbun shuppansha},
DATE = {1974/1977}
}
First we need to extend biblatex's data model. Add a file named biblatex-dm.cfg with something like:
% Declare transliterated/translated fields
% To guess the type cf. https://github.com/plk/biblatex/blob/dev/tex/latex/biblatex/blx-dm.def
\DeclareDatamodelFields[type=field, datatype=literal]{title_romanised}
\DeclareDatamodelFields[type=list, datatype=literal]{location_romanised}
\DeclareDatamodelFields[type=list, datatype=name]{editor_romanised, author_romanised}
%Fields should be now assigned relevant entry types, but it seems not to be actually needed...
%\DeclareDatamodelEntryfields{title_romanised, editor_romanised, author_romanised,...}
Finally, we have to define a style that uses the fields as desired. For example, to print romanised title and editor when available create a file named addromanised.bbx with:
\ProvidesFile{addromanised.bbx}
%A base style
\RequireBibliographyStyle{numeric}
%Check what bibmacros need to be rewritten. See the style you are using as a base to find out the macros. They usually come from:
%https://mirror.hmc.edu/ctan/macros/latex/exptl/biblatex/latex/bbx/standard.bbx
%https://github.com/plk/biblatex/blob/dev/tex/latex/biblatex/biblatex.def
\renewbibmacro*{title}{%
\iffieldundef{title_romanised}{%
\printfield{title}%
}{%
\printfield{title} (\printfield{title_romanised})%
}%
}%
\renewbibmacro*{editor+others}{%
\ifboolexpr{
test \ifuseeditor
and
not test {\ifnameundef{editor}}
}
{\ifnameundef{editor_romanised}{%
\printnames{editor} %
}{%
\printnames{editor} (\printnames{editor_romanised}) %
}%
\setunit{\printdelim{editortypedelim}}%
\usebibmacro{editor+othersstrg}%
\clearname{editor}}
{}}
This file is easy to extend to add more field or to add a translation as well or to replace them by their romanised versions.
The following code shows how the style is used with LuaLaTeX:
\documentclass{article}
\usepackage{fontspec}
\usepackage{luatexja-fontspec}
\usepackage{polyglossia}
\setdefaultlanguage{english}
\usepackage[backend=biber,bibstyle=addromanised]{biblatex}
\addbibresource{test.bib}
\begin{document}
\nocite{*}
\printbibliography
\end{document}

Creating an additional style which adds katakana fields instead will solve the other half of the problem.
As a final note, if you are sorting by any of these fields, you may want to use the romanizations when they are available. For example, to adapt the nyvt sorting you could add the following code to your style:
\DeclareSortingScheme{romanisednyvt}{
\sort{
\field{presort}
}
\sort[final]{
\field{sortkey}
}
\sort{
\field{sortname}
\field{author_romanised}
\field{author}
\field{editor_romanised}
\field{editor}
\field{translator}
\field{sorttitle}
\field{title_romanised}
\field{title}
}
\sort{
\field{sortyear}
\field{year}
}
\sort{
\field{volume}
\literal{0}
}
\sort{
\field{sorttitle}
\field{title}
}
}
And load it with \usepackage[backend=biber,bibstyle=addromanised sorting=romanisednyvt]{biblatex}