This can be solved by creating a new name format that formats the first name(s) as just the very first initial:
% Format for VeryFirstInitial - LastName
\DeclareNameFormat{firstfirstinit-last}{%
\usebibmacro{name:first-last}{#1}{\firstinit{#4}\adddot}{#5}{#7}%
\usebibmacro{name:andothers}}
To do this, I use a custom macro that identifies just the very first initial of the first names (courtesy of @StevenBSegletes, Typeset just the first letter in a group):
% Helper function to get initial letter
\def\firstinit#1{\justfirst#1\relax}
\def\justfirst#1#2\relax{#1}
Then biblatex is set to use first initials in the bibliography and just the very first initial in in-text citations:
% Set format for sortname (bibliography) and labelname (citation)
\DeclareNameAlias{sortname}{firstinits-last}
\DeclareNameAlias{labelname}{firstfirstinit-last}
The Result

MWE
\documentclass[]{article}
\usepackage{filecontents}
\begin{filecontents*}{bib.bib}
@article{jdoe,
author = {John Paul Peter Julian Doe},
journal = {Journal},
title = {Title},
year = 2014,
pages = 111--222,
}
\end{filecontents*}
\usepackage[style=authoryear]{biblatex}
\addbibresource{bib.bib}
% Helper function to get initial letter
\def\firstinit#1{\justfirst#1\relax}
\def\justfirst#1#2\relax{#1}
% Format for FirstInitials - LastName (standard implementation)
\DeclareNameFormat{firstinits-last}{%
\usebibmacro{name:first-last}{#1}{#4}{#5}{#7}%
\usebibmacro{name:andothers}}
% Format for VeryFirstInitial - LastName
\DeclareNameFormat{firstfirstinit-last}{%
\usebibmacro{name:first-last}{#1}{\firstinit{#4}\adddot}{#5}{#7}%
\usebibmacro{name:andothers}}
% Set format for sortname (bibliography) and labelname (citation)
\DeclareNameAlias{sortname}{firstinits-last}
\DeclareNameAlias{labelname}{firstfirstinit-last}
\begin{document}
\noindent Citation: \cite{jdoe}.
\printbibliography[]
\end{document}
{{John Paul Peter Julian} Doe}, but that will not work if you want all initials in the bibliography and only "J. Doe" in citations. – moewe Mar 04 '14 at 18:22.bibfile. – ienissei Mar 04 '14 at 23:19