To get rid of the complete label simply add the following lines in your preamble (possibility 1):
\makeatletter
\renewcommand\@biblabel[1]{} % <========================== possibility 1
%\renewcommand\@biblabel[1]{\textbullet} % <============== possibility 2
\makeatother
If you want instead the label an for example textbullet to mark the beginning of a new bib entry you can use possibility 2 like
\makeatletter
%\renewcommand\@biblabel[1]{} % <========================== possibility 1
\renewcommand\@biblabel[1]{\textbullet} % <============== possibility 2
\makeatother
With the following MWE (uses filecontents to add the bib file in the compilable mwe)
\begin{filecontents*}{\jobname.bib}
@Book{Goossens,
author = {Goossens, Michel and Mittelbach, Frank and
Samarin, Alexander},
title = {The LaTeX Companion},
edition = {1},
publisher = {Addison-Wesley},
location = {Reading, Mass.},
year = {1994},
}
@Book{adams,
title = {The Restaurant at the End of the Universe},
author = {Douglas Adams},
series = {The Hitchhiker's Guide to the Galaxy},
publisher = {Pan Macmillan},
year = {1980},
}
@article{feynman,
title = {Very High-Energy Collisions of Hadrons},
author = {Richard P. Feynman},
journal = {Phys. Rev. Lett.},
volume = {23},
issue = {24},
pages = {1415--1417},
year = {1969},
month = {Dec},
doi = {10.1103/PhysRevLett.23.1415},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.23.1415},
publisher = {American Physical Society},
}
@article{MyArticle,
title = {A Fancy Title},
author = {Doe, John},
journal = {Prestigous Journal},
volume = {2},
issue = {3},
pages = {038952},
year = {2020},
month = {Jul},
}
\end{filecontents*}
\documentclass[11pt,a4paper]{moderncv}
\moderncvstyle{classic}
\moderncvcolor{black}
\usepackage[scale=0.75]{geometry}
\name{John}{Doe}
\makeatletter
\renewcommand@biblabel[1]{} % <========================== possibility 1
%\renewcommand@biblabel[1]{\textbullet} % <============== possibility 2
\makeatother
\begin{document}
\makecvtitle
\nocite{*}
\bibliographystyle{apsrev4-1} %
\bibliography{\jobname}
\end{document}
you get the resulting pdf

With possibility 2 you get the following resulting pdf:
