How do I write "LaTeX" in LaTeX with the first letter bolded?

Note: There's a similar question and answer here: Color up each letter of \LaTeX word

You can find the definitions of \TeX, \LaTeX and \LaTeXe in latex.ltx (which is really, really surprising ;-) )

Easiest way is to use the definitions and save them as new commands, say \BLaTeX for Bold \LaTeX ;-)

However, the kerning is wrong initially, so I changed it slightly -- please provide own values for the kerning if the given example does not really fit yet regarding personal taste.

\documentclass{article}

\usepackage{xcolor}
\makeatletter
\newcommand{\Lletterstyle}[1]{%
  \textcolor{red}{\textbf{#1}}%
}
\DeclareRobustCommand{\BLaTeX}{\Lletterstyle{L}\kern-.35em%
  {\sbox\z@ T%
    \vbox to\ht\z@{\hbox{\check@mathfonts
        \fontsize\sf@size\z@
        \math@fontsfalse\selectfont
        A}%
      \vss}%
  }%
  \kern-.15em%
  \TeX%
}
\DeclareRobustCommand{\BLaTeXe}{\mbox{\m@th
  \if b\expandafter\@car\f@series\@nil\boldmath\fi
  \BLaTeX\kern.15em2$_{\textstyle\varepsilon}$}}
\makeatother

\begin{document}

\BLaTeX\ or \LaTeX

\BLaTeXe\ or \LaTeXe

Huge:\huge

\BLaTeX\ or \LaTeX

\BLaTeXe\ or \LaTeXe


\end{document}

You can make a small extension to the metalogo package, which enables you to choose a different initial “L”.

\documentclass{article}
\usepackage{metalogo}
\usepackage{xpatch}

\makeatletter
\newcommand{\setLaTeXL}[1]{\def\xl@LaTeXL{#1}}
\xpatchcmd{\LaTeX}{L}{\xl@LaTeXL}{}{}
\makeatother
% initialize
\setLaTeXL{L}

\newcommand{\BLaTeX}{{\setLaTeXL{\textbf{L}}\LaTeX}}

\begin{document}

\LaTeX \BLaTeX \LaTeX

\setLaTeXL{\textbf{L}}

\LaTeX

\setLaTeXL{{\usefont{U}{rsfso}{m}{n}L}}
\setlogokern{La}{-.2em}

\LaTeX

\end{document}

As you see, the commands obey the usual scoping rules. If you want a global redefinition, issue \setLaTeXL{\textbf{L}} in the preamble. Otherwise define \BLaTeX as shown and you'll have available both versions.