The documentation of the ledmac package explains how to build a command \killnumber to suppress the line number in a note; in the following code I implemented (and used) this command.
Using the \lemma command in the first argument of \edtext you can change the text used as lemma from "Blindtext" to (the desired) "Title:".
I also show you how to redefine the \rbracket command to suppress the symbol "]" in the first note (according to your request, this symbol shouldn't appear in the first note); of course, \rbracket is then redefined again to get its original meaning.
\documentclass{article}
\usepackage{ledmac,ledpar}
\firstlinenum{1}\linenumincrement{1}
% a command to suppress line number for a note (see the ledmac documentation)
\newcommand*{\killnumber}{\linenum{|-1|||-1||}}
\makeatletter
\def\printlines#1|#2|#3|#4|#5|#6|#7|{\begingroup
\ifnum#2=-1
\ledplinenumfalse%
\renewcommand\symplinenum{\hspace*{0.4em}}% this will align the unnumbered footnote text
% with the text of the first line of numbered footnotes.
% Change to -0.5em to get the unnumbered footnote text
% aligned with the document left margin
\fi%
\setprintlines{#1}{#2}{#3}{#4}{#5}{#6}%
\ifl@d@pnum #1\fullstop\fi
\ifledplinenum \linenumrep{#2}\else \symplinenum\fi
\ifl@d@ssub \fullstop \sublinenumrep{#3}\fi
\ifl@d@dash \endashchar\fi
\ifl@d@pnum #4\fullstop\fi
\ifl@d@elin \linenumrep{#5}\fi
\ifl@d@esl \ifl@d@elin \fullstop\fi \sublinenumrep{#6}\fi
\endgroup}
\makeatother
\begin{document}
\symplinenum
\beginnumbering
\setstanzaindents{0,0,0,0,0}
\renewcommand*{\rbracket}{}% suppress the symbol "]" in the note
\stanza
The \edtext{Blindpoem}%
{\killnumber\lemma{Title:}\Bfootnote{Some note.}}
\skipnumbering\&
\renewcommand*{\rbracket}{\textnormal{\thinspace]}}% restore the symbol "]" for the notes
\stanza
This is &
a stupid &
and short &
\edtext{blindpoem.}{\Bfootnote{Yes, it is.}}
\&
\endnumbering
\end{document}
EDIT: as suggested by Alan Munn, I've added a redefinition of \symplinenum to control the alignment of the unnumbered footnote.