How can I get this symbol without using bbold?

How about dsfont?

\documentclass{article}
\usepackage{dsfont}
\usepackage{amssymb}
\begin{document}
$\mathds{1}$ and $\mathbb{B}$ or $\mathds{B}$
\end{document}

The modern toolchain, with unicode-math, lets you select any TrueType or OpenType font for blackboard bold, or any subset of blackboard bold. For example,

\setmathfont[Scale = MatchUppercase, range=\Bbbone]{XITS Math}

changes only that one symbol, while

\setmathfont[Scale = MatchUppercase, range=bb]{STIX Two Math}

changes the entire blackboard bold alphabet.

You can just borrow the glyph from the bbold font.

\documentclass{article}
\usepackage{amsmath,amssymb}

\newcommand{\bbone}{\text{\usefont{U}{bbold}{m}{n}1}}
\MakeRobust{\bbone}

\begin{document}

$\bbone\in\mathbb{R}$

\end{document}

The “robustness” is needed for uses in moving arguments (sectional titles or captions).