There are three problems: the line number is in the middle of the paragraph, the paragraph is not justified and the line skip between the paragraph and the lines \begin{document} and \end{document} is to small.
The first can be solved with the optional argument [t] to \pbox, which set the baseline of the \pbox to its first line.
The third problem can be solved by adding \strut to the beginning and end of the paragraph.
For the second problem, justifying the paragraph, a little bit of help from this answer (the same as in samcarters answer) is needed. But this sets the fontdimens globally, which may not be wanted. Therefore I wrote macros for storing, setting and restoring them. And to avoid having to type all of this every time, there is also a macro \justifiedtt with the same syntax as \pbox (which is uses internally).
Here are the results of the different parts of the solution (I just shortened the text a little):

And here is the code:
\documentclass{article}
\usepackage{fancyvrb}
\usepackage{ragged2e}
\usepackage{lipsum}
\usepackage{pbox}
\makeatletter
\newdimen\@orig@fdiii
\newdimen\@orig@fdiv
\newcount\@orig@hych
\newcommand*\@set@interword{%
\@orig@fdiii=\fontdimen3\font
\@orig@fdiv=\fontdimen4\font
\@orig@hych=\hyphenchar\font
\fontdimen3\font=0.2em% interword stretch
\fontdimen4\font=0.1em% interword shrink
\hyphenchar\font=`\-% allowing hyphenation
}
\newcommand*\@restore@interword{%
\fontdimen3\font=\@orig@fdiii
\fontdimen4\font=\@orig@fdiv
\hyphenchar\font=\@orig@hych
}
\newcommand{\justifiedtt}[3][c]{\pbox[#1]{#2}{\ttfamily\@set@interword\strut#3\strut\@restore@interword}}
\makeatother
\begin{document}
\noindent
Original:
\begin{Verbatim}[numbers=left,fontsize=\bf,commandchars=\^\#\*,baselinestretch=1,firstnumber=1,stepnumber=1]
\begin{document}
^pbox#^textwidth*#The flowers of most species have five petals, with the exception of Rosa sericea, which usually has only four. Each petal is divided into two distinct lobes and is usually white or pink, though in a few species yellow or red.*
\end{document}
\end{Verbatim}
\noindent
With \verb|[t]|:
\begin{Verbatim}[numbers=left,fontsize=\bf,commandchars=\^\#\*,baselinestretch=1,firstnumber=1,stepnumber=1]
\begin{document}
^pbox[t]#^textwidth*#The flowers of most species have five petals, with the exception of Rosa sericea, which usually has only four. Each petal is divided into two distinct lobes and is usually white or pink, though in a few species yellow or red.*
\end{document}
\end{Verbatim}
\noindent
With \verb|\strut| at start and end:
\begin{Verbatim}[numbers=left,fontsize=\bf,commandchars=\^\#\*,baselinestretch=1,firstnumber=1,stepnumber=1]
\begin{document}
^pbox#^textwidth*#^strut#*The flowers of most species have five petals, with the exception of Rosa sericea, which usually has only four. Each petal is divided into two distinct lobes and is usually white or pink, though in a few species yellow or red.^strut*
\end{document}
\end{Verbatim}
\noindent
With \verb|\justifiedtt|:
\begin{Verbatim}[numbers=left,fontsize=\bf,commandchars=\^\#\*,baselinestretch=1,firstnumber=1,stepnumber=1]
\begin{document}
^justifiedtt[t]#^textwidth*#The flowers of most species have five petals, with the exception of Rosa sericea, which usually has only four. Each petal is divided into two distinct lobes and is usually white or pink, though in a few species yellow or red.*
\end{document}
\end{Verbatim}
\noindent
\verb|\justifiedtt| outside \verb|Verbatim| also works:
\noindent
\justifiedtt[t]{\textwidth}{The flowers of most species have five petals, with the exception of Rosa sericea, which usually has only four. Each petal is divided into two distinct lobes and is usually white or pink, though in a few species yellow or red.}
\end{document}
\begin{document}and\end{document}twice on purpose? – AML May 08 '18 at 11:43verbatim, or do you just want it to look a certain way? You might be better off making it look likeverbatimwithout actually usingverbatim. – AML May 08 '18 at 17:15verbatimorVerbatim. Why do you need it? – Werner May 10 '18 at 16:30