How to split the bibliography alphabetically?

You can create a category for each letter in the alphabet and, with \AtDataInput, add entries to each category on the basis of the sortinit field.

\documentclass{book}
\usepackage[style=alphabetic]{biblatex}

\addbibresource{biblatex-examples.bib}
\nocite{angenendt,bertram,doody,gillies}

% user-level test for skipbib enabled (e.g. related entry matuz:doody)
\makeatletter
\def\ifskipbib{\iftoggle{blx@skipbib}}
\makeatother

\def\initlist{}
\forcsvlist{\listadd\initlist}{A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}
\forlistloop{\DeclareBibliographyCategory}{\initlist}
\renewcommand*{\do}[1]{\defbibheading{#1}{\section*{#1}}}
\dolistloop{\initlist}
\AtDataInput{\ifskipbib{}{\addtocategory{\thefield{sortinit}}{\thefield{entrykey}}}}

\begin{document}
\printbibheading
\bibbycategory
\end{document}

Note that we need to access some internals to avoid entries that are skipped in the bibliography. I keep forgetting to make these toggle values available to the user, but we'll get around to it soon.

Here a hack of the internal bibitem:

\documentclass[]{scrartcl}

\usepackage[style=alphabetic]{biblatex}
\makeatletter
\def\blx@head@tempa{0}
\def\blx@bibitem#1{%
  \blx@ifdata{#1}
    {\begingroup
     \blx@getdata{#1}%
     \blx@imc@iffieldequals{sortinit}\blx@head@tempa{}{\item[]\textbf{\thefield{sortinit}}}%
       \global\let\blx@head@tempa\abx@field@sortinit%
     \blx@bibcheck
       \global\let\blx@noitem\@empty
     \iftoggle{blx@skipentry}{}{%
       \blx@setoptions@type\abx@field@entrytype
       \blx@setoptions@entry
       \blx@thelabelnumber
       \blx@addprefixnumber
       \addtocounter{instcount}\@ne
       \csuse{blx@item@\blx@theenv}\relax
       \blx@initsep
       \blx@namesep
       \csuse{blx@hook@bibitem}%
       \blx@execute
       \blx@initunit
       \blx@anchor
       \blx@beglangbib
       \bibsentence
       \blx@pagetracker
       \blx@driver\abx@field@entrytype
       \blx@postpunct
       \blx@endlangbib}%
     \endgroup}
    {}}
\makeatother
\addbibresource{biblatex-examples.bib}
\begin{document}
\nocite{*}
\printbibliography
\end{document}

Although the marking of alphabetical sections with "heading letters" is sometimes used for indexes, I have never encountered such letters in bibliographies. I suggest to only add extra spacing between alphabetical sections; with biblatex, this can be done by simply setting the \bibinitsep length to a positive value.

\documentclass{book}

\usepackage[style=authoryear]{biblatex}

\setlength{\bibinitsep}{\baselineskip}

\usepackage{filecontents}

\begin{filecontents}{\jobname.bib}
@misc{A01,
  author = {Author, A.},
  year = {2001},
  title = {Alpha},
}
@misc{A02,
  author = {Author, A.},
  year = {2002},
  title = {And now for something completely different},
}
@misc{B02,
  author = {Buthor, B.},
  year = {2002},
  title = {Bravo},
}
\end{filecontents}

\addbibresource{\jobname.bib}

\nocite{*}

\begin{document}

\printbibliography

\end{document}