There you go.
\documentclass{amsart}
\DeclareSymbolFont{ntxletters}{OML}{ntxmi}{m}{it}
\SetSymbolFont{ntxletters}{bold}{OML}{ntxmi}{b}{it}
\DeclareMathSymbol{\phi}{\mathord}{ntxletters}{30}
\usepackage{bm}
\begin{document}
\Huge
\[\phi, \bm{\phi}\]
\end{document}

Thanks to @marmot pointing out this previous answer by @AlanMunn. As @AlanMunn said in that answer, one needs some basic knowledge about font declarations before performing the trick. This key line of code in newtxmath.sty:
%\DeclareMathSymbol{\phi}{\mathord}{letters}{30}
tells us that we should be looking for lines that declare letters. Indeed, we find
%%%%%%%%%%%%%%%
% Math Italic %
%%%%%%%%%%%%%%%
... ... ...
\DeclareSymbolFont{letters}{OML}{ntxmi}{m}{it}
\SetSymbolFont{letters}{bold}{OML}{ntxmi}{b}{it}
... ... ...
Thus, the suggested solution.
ntxmi! Although I know the method, but I didn't findntxmi! – M. Logic Oct 02 '18 at 11:37