I printed out a stepped counter in the loop for the problem number (and another counter for the bubble label) and changed the square \rule to a rotated "0", scaled and stretched appropriately. You can change the size via the numerical arguments to \scalebox{1.4}[1.5]{}. I also made it two column.
EDITED to provide sample filled block.
\documentclass[a4paper,twocolumn]{article}
\usepackage{tikz,graphicx}
\usepackage[usestackEOL]{stackengine}
\newcommand{\repeatntimes}[2]{
\newcount\i
\i=0
\newtoks\ans
\loop
\ans=\expandafter{\the\ans #2}
\advance\i by 1
\ifnum\i<#1\repeat
\the\ans
}
\newcommand{\countRepeatntimes}[2]{
\newcount\i
\i=0
\newtoks\ans
\loop
\advance\i by 1
\ans=\expandafter{\the\ans #2}
\ifnum\i<#1\repeat
\the\ans
}
\newcounter{problem}
\newcounter{choice}
\newcommand{\generateTable}[1]{%
\countRepeatntimes{#1}{\stepcounter{problem}\makebox[2ex][r]{\theproblem.}%\indent
\setcounter{choice}{0}%
\repeatntimes{4}{\stepcounter{choice}\textcolor{black!35}{%
\raisebox{-1.5pt}{\scalebox{1.5}[1.8]{\stackinset{c}{}{c}{}{%
\scalebox{.6}{\tiny \Alph{choice}}}{\rotatebox{90}{0}}}}} }\par
}
}
\def\sampleblock{%
\makebox[5.1ex]{}
\stepcounter{choice}\textcolor{black!35}{%
\raisebox{-1.5pt}{\scalebox{1.5}[1.8]{\stackinset{c}{}{c}{}{%
\scalebox{.6}{\tiny \Alph{choice}}}{\rotatebox{90}{0}}}}}
\stepcounter{choice}\textcolor{black!35}{%
\raisebox{-1.5pt}{\scalebox{1.5}[1.8]{\stackinset{c}{}{c}{}{%
\scalebox{.6}{\tiny \Alph{choice}}}{\rotatebox{90}{0}}}}}
\stepcounter{choice}\textcolor{black!35}{%
\smash{\raisebox{-1.5pt}{\scalebox{1.5}[1.8]{\stackinset{c}{}{c}{-1pt}{%
\scalebox{6}[3.5]{\color{black}$\cdot$}}{\rotatebox{90}{0}}}}}}
\stepcounter{choice}\textcolor{black!35}{%
\raisebox{-1.5pt}{\scalebox{1.5}[1.8]{\stackinset{c}{}{c}{}{%
\scalebox{.6}{\tiny \Alph{choice}}}{\rotatebox{90}{0}}}}}
\par}
\voffset=\dimexpr\voffset+.5in
\textheight=\dimexpr\textheight-.5in
\begin{document}
\smash{\Shortstack[l]{%
Name \underline{\hspace{2.4in}} Class\underline{\hspace{1.2in}}
Date\underline{\hspace{1.2in}}\
\textcolor{black!50}{\rule{5.9in}{2ex}}\
\rule[2ex]{10ex}{2ex}\sffamily\itshape\Huge Bubble Answer Sheet\
\strut\
\sampleblock\
\rule{0ex}{4pt}\}%
}\vspace{-\baselineskip}\par
\def\qCount{80}
\generateTable{\qCount}
\end{document}


SUPPLEMENT
A comment requested a version with circular choices:
\documentclass[a4paper,twocolumn]{article}
\usepackage{tikz,graphicx}
\usepackage[usestackEOL]{stackengine}
\newcommand{\repeatntimes}[2]{
\newcount\i
\i=0
\newtoks\ans
\loop
\ans=\expandafter{\the\ans #2}
\advance\i by 1
\ifnum\i<#1\repeat
\the\ans
}
\newcommand{\countRepeatntimes}[2]{
\newcount\i
\i=0
\newtoks\ans
\loop
\advance\i by 1
\ans=\expandafter{\the\ans #2}
\ifnum\i<#1\repeat
\the\ans
}
\newcounter{problem}
\newcounter{choice}
\newcommand{\generateTable}[1]{%
\countRepeatntimes{#1}{\stepcounter{problem}\makebox[2ex][r]{\theproblem.}%\indent
\setcounter{choice}{0}%
\repeatntimes{4}{\stepcounter{choice}\textcolor{black!35}{%
\raisebox{0.5pt}{\scalebox{1.0}{\stackinset{c}{}{c}{}{%
\scalebox{.6}{\footnotesize \Alph{choice}}}{$\bigcirc$}}}} }\par
}
}
\def\sampleblock{%
\makebox[5.1ex]{}
\stepcounter{choice}\textcolor{black!35}{%
\raisebox{-1.5pt}{\scalebox{1.0}{\stackinset{c}{}{c}{}{%
\scalebox{.6}{\footnotesize \Alph{choice}}}{$\bigcirc$}}}}
\stepcounter{choice}\textcolor{black!35}{%
\raisebox{-1.5pt}{\scalebox{1.0}{\stackinset{c}{}{c}{}{%
\scalebox{.6}{\footnotesize \Alph{choice}}}{$\bigcirc$}}}}
\stepcounter{choice}\textcolor{black!35}{%
\smash{\raisebox{-1.5pt}{\scalebox{1.0}{\stackinset{c}{}{c}{-2.5pt}{%
\scalebox{8}{\color{black}$\cdot$}}{$\bigcirc$}}}}}
\stepcounter{choice}\textcolor{black!35}{%
\raisebox{-1.5pt}{\scalebox{1.0}{\stackinset{c}{}{c}{}{%
\scalebox{.6}{\footnotesize \Alph{choice}}}{$\bigcirc$}}}}
\par}
\voffset=\dimexpr\voffset+.5in
\textheight=\dimexpr\textheight-.5in
\begin{document}
\smash{\Shortstack[l]{%
Name \underline{\hspace{2.4in}} Class\underline{\hspace{1.2in}}
Date\underline{\hspace{1.2in}}\
\textcolor{black!50}{\rule{5.9in}{2ex}}\
\rule[2ex]{10ex}{2ex}\sffamily\itshape\Huge Bubble Answer Sheet\
\strut\
\sampleblock\
\rule{0ex}{4pt}\}%
}\vspace{-\baselineskip}\par
\def\qCount{80}
\generateTable{\qCount}
\end{document}
