How to eliminate number labels from two-column bibliography

I found a code snippet for a two-column bibliography in this answer:

usepackage{multicol}

makeatletter
renewenvironment{thebibliography}[1]
     {begin{multicols}{2}[section*{refname}]%
      @mkboth{MakeUppercaserefname}{MakeUppercaserefname}%
      list{@biblabel{@arabicc@enumiv}}%
           {settowidthlabelwidth{@biblabel{#1}}%
            leftmarginlabelwidth
            advanceleftmarginlabelsep
            @openbib@code
            usecounter{enumiv}%
            letp@enumiv@empty
            renewcommandtheenumiv{@arabicc@enumiv}}%
      sloppy
      clubpenalty4000
      @clubpenalty clubpenalty
      widowpenalty4000%
      sfcode`.@m}
     {def@noitemerr
       {@latex@warning{Empty `thebibliography' environment}}%
      endlistend{multicols}}
makeatother

This basically does what I want (i.e. is in two columns, so takes up less space) except that each item is preceded by [1], [2], …
Since I’m using the bibliography in moderncv I don’t really need labels since there are no citations in the text. If labels are hard to avoid, I’d prefer something like a bullet.

I guess this might make things more compicated, but for better or worse I am currently using plainyr-rev.bst also. That’s not vital though; the bblography only contains a dozen or so items and I could just change the labels and sort by those, probably.

makeatletter
ifthenelse{boolean{twocolbib}}{
renewenvironment{thebibliography}[1]
     {begin{multicols}{2}[section*{refname}]%
      @mkboth{MakeUppercaserefname}{MakeUppercaserefname}%
      list{}
           {settowidthlabelwidth{@biblabel{#1}}%
            leftmarginlabelwidth
            advanceleftmarginlabelsep
            @openbib@code
            usecounter{enumiv}%
            letp@enumiv@empty
            renewcommandtheenumiv{@arabicc@enumiv}}%
      sloppy
      clubpenalty4000
      @clubpenalty clubpenalty
      widowpenalty4000%
      sfcode`.@m}
     {def@noitemerr
       {@latex@warning{Empty `thebibliography' environment}}%
      endlistend{multicols}}
}{}
makeatother