Here's an edited version of your example that should theoretically work with all engines:
\documentclass{article}
\usepackage{ifluatex,ifxetex}
\ifluatex\else\ifxetex\else
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\fi\fi
\usepackage[english]{babel}
\usepackage{ebgaramond}
\begin{document}
\begin{itemize}
\item Here is some plain text in Garamond
\end{itemize}
\end{document}
However, there is a bug in the distributed file TS1EBGaramond-OsF.fd where the last few lines have LF instead of OsF: it should be
%% Generated by autoinst on 2013/02/13
%%
\ProvidesFile{TS1EBGaramond-OsF.fd}
[2013/02/13 (autoinst) Font definitions for TS1/EBGaramond-OsF.]
\expandafter\ifx\csname EBGaramond@scale\endcsname\relax
\let\EBGaramond@@scale\@empty
\else
\edef\EBGaramond@@scale{s*[\csname EBGaramond@scale\endcsname]}%
\fi
\DeclareFontFamily{TS1}{EBGaramond-OsF}{}
\DeclareFontShape{TS1}{EBGaramond-OsF}{m}{n}{
<-> \EBGaramond@@scale EBGaramond12-Regular-osf-ts1
}{}
\DeclareFontShape{TS1}{EBGaramond-OsF}{m}{it}{
<-> \EBGaramond@@scale EBGaramond12-Italic-osf-ts1
}{}
\DeclareFontShape{TS1}{EBGaramond-OsF}{m}{sl}{ <-> ssub * EBGaramond-OsF/m/it }{}
\DeclareFontShape{TS1}{EBGaramond-OsF}{b}{n}{ <-> ssub * EBGaramond-OsF/m/n }{}
\DeclareFontShape{TS1}{EBGaramond-OsF}{b}{it}{ <-> ssub * EBGaramond-OsF/m/it }{}
\DeclareFontShape{TS1}{EBGaramond-OsF}{b}{sl}{ <-> ssub * EBGaramond-OsF/m/it }{}
\DeclareFontShape{TS1}{EBGaramond-OsF}{bx}{n}{ <-> ssub * EBGaramond-OsF/m/n }{}
\DeclareFontShape{TS1}{EBGaramond-OsF}{bx}{it}{ <-> ssub * EBGaramond-OsF/m/it }{}
\DeclareFontShape{TS1}{EBGaramond-OsF}{bx}{sl}{ <-> ssub * EBGaramond-OsF/m/it }{}
\endinput
but the last seven \DeclareFontShape declarations have LF instead of OsF in all places. Probably that part has been copied by the similar TS1EBGaramond-LF.fd and not edited.
Therefore you get the error message you mention when compiling with pdflatex, because the font description file refers to an unknown font family.
There are some possible workarounds.
Copy the distributed TS1EBGaramond-OsF.fd file to the document directory and edit it so that it appears as above.
Directly edit the distributed file (risky)
Add the necessary code to keep pdflatex happy:
\documentclass[english]{article}
\usepackage{ifluatex,ifxetex}
\ifluatex\else\ifxetex\else
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\fi\fi
\usepackage{babel}
\usepackage{ebgaramond}
\ifluatex\else\ifxetex\else
\normalfont
\makeatletter
\input{TS1EBGaramond-LF.fd}
\input{TS1EBGaramond-OsF.fd}
\makeatother
\DeclareFontShape{TS1}{EBGaramond-OsF}{m}{sl}{ <-> ssub * EBGaramond-OsF/m/it }{}
\DeclareFontShape{TS1}{EBGaramond-OsF}{b}{n}{ <-> ssub * EBGaramond-OsF/m/n }{}
\DeclareFontShape{TS1}{EBGaramond-OsF}{b}{it}{ <-> ssub * EBGaramond-OsF/m/it }{}
\DeclareFontShape{TS1}{EBGaramond-OsF}{b}{sl}{ <-> ssub * EBGaramond-OsF/m/it }{}
\DeclareFontShape{TS1}{EBGaramond-OsF}{bx}{n}{ <-> ssub * EBGaramond-OsF/m/n }{}
\DeclareFontShape{TS1}{EBGaramond-OsF}{bx}{it}{ <-> ssub * EBGaramond-OsF/m/it }{}
\DeclareFontShape{TS1}{EBGaramond-OsF}{bx}{sl}{ <-> ssub * EBGaramond-OsF/m/it }{}
\fi\fi
\begin{document}
\begin{itemize}
\item Here is some plain text in Garamond
\end{itemize}
\end{document}
In any case, you should mention the problem to the package maintainer.