Instead of your . use an empty pair of {}.
Instead of that \qquad hack I present
text align/right indent=1cm
That, sadly, does not work with em units …
Code
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations.text}
\begin{document}
\begin{tikzpicture}
\coordinate (a) at (0,0);
\coordinate (b) at (6,0);
\draw[->, >=latex, blue!20!white, bend left=20, line width=15pt] (a) to (b) ;
\draw [name=reusepath,bend left=20, decoration={raise=-0.8ex,text along path, text={{$start$}{}}}, decorate] (a) to (b);
\draw [bend left=20, decoration={raise=-0.8ex,text along path, text={{$end$}}, text align/right indent=1cm, text align=right}, decorate] (a) to (b);
\end{tikzpicture}
\end{document}
Output

From the beamer manual
It is only possible to typeset text in math mode under considerable restrictions. Math mode is entered and exited using any character of category code 3 (e.g., in plain TeX this is $). Math subscripts and superscripts need to be contained within braces (e.g., {^y_i}) as do commands like \times or \cdot. However, even modestly complex mathematical typesetting is unlikely to be successful along a path (or even desirable).
Update
I allowed myself to "clean" your code a little bit, so that only one path is generated and the decorations are declared as a postaction.
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations.text,intersections}
\begin{document}
\begin{tikzpicture}
\coordinate (a) at (0,0);
\coordinate (b) at (6,0);
\draw[->, >=latex,
blue!20!white,
bend left=20,
line width=15pt,
postaction={decorate,decoration={
raise=-0.8ex,
text along path,
text={{$start$}{}}
}
},
postaction={decorate,decoration={
raise=-0.8ex,
text along path,
text={{$end$}},
text align/right indent=1cm,
text align=right
}
}
] (a) to (b) ;
\end{tikzpicture}
\end{document}
{{$start$}.}and{{$end$}.}– Neil G Oct 01 '12 at 02:20