= Solution
Choose a positive reference <biological growth factor> concentration $G_{ref}$, for example its <concentration> ahead of the <travelling wave>. Set
$$
T=T_0t,\quad X=X_0x,\quad G=G_{ref}g,\quad B=B_0b,
$$
where
$$
\boxed{T_0=\frac1{\nu G_{ref}},\qquad X_0=\sqrt{\frac D{\nu G_{ref}}},\qquad B_0=\frac{\nu G_{ref}}\mu.}
$$
The <chain rule> then transforms the equations into
$$
b_t=\frac{DT_0}{X_0^2}b_{xx}+\nu G_{ref}T_0gb,\qquad g_t=-\mu B_0T_0gb.
$$
Each displayed coefficient is one with the chosen scales. Hence the <dimensionless> system is
$$
\boxed{b_t=b_{xx}+gb,\qquad g_t=-gb.}
$$
The free choice of $G_{ref}$ expresses the freedom to normalize the as-yet unspecified <concentration> scale.
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