What I mean is that $\mathbb{CRZ}$ etc. are used for different classes of numbers, allowing me to do stuff like this:
$$f:\mathbb{R}\to\mathbb{R}$$ $$f:x\mapsto 3x$$
But say I have an expression like this:
$$g:x\mapsto x>4$$
What symbol would you use to represent a boolean result? a $\mathbb B$?
According to this Wikipedia page, the most common representation is $\{0,1\}$. Alternatives include $\{\text{false},\text{true}\}$, $\{\mathrm F,\mathrm T\}$, $\{\bot,\top\}$, and $\Bbb B$.
If you wish to use either the symbol $\Bbb B$ or $\mathbf B$, you can define it yourself to prevent any ambiguity. What really matters is that the notation is readable and understandable.