Here are two options:
Set the smaller box (your premise \AxiomC
) in a box of the same width as the larger box (your conclusion \UnaryInfC
), only left-aligned. This can be achieved using \makebox[<width>][l]{...}
; or
Use \phantom{<stuff>}
to remove <stuff>
from the display but still have the appropriate space allocated for it.

\documentclass{article}
\usepackage{bussproofs}% http://ctan.org/pkg/bussproofs
\newlength{\mylen}
\begin{document}
\begin{prooftree}
\settowidth{\mylen}{$\neg A \lor \neg B$}%
\AxiomC{\makebox[\mylen][l]{$\neg A$}}
\UnaryInfC{$\neg A \lor \neg B$}
\end{prooftree}
\begin{prooftree}
\AxiomC{$\neg A \phantom{\:{\lor}\:\neg B}$}
\UnaryInfC{$\neg A \lor \neg B$}
\end{prooftree}
\end{document}
In the first example, the width of the conclusion is stored in \mylen
(a new length) via \settowidth
. \mylen
is then used to provide the box width for the premise.
In the second example, a minor correction for the spacing around the binary operator \lor
is performed by adding \:
around the now atomized {\lor}
.