  We study static black holes in scalar-Gauss-Bonnet (sGB) gravity with a
massive scalar field as an example of higher curvature gravity. The scalar mass
introduces an additional scale and leads to a strong suppression of the scalar
field beyond its Compton wavelength. We numerically compute sGB black hole
spacetimes and scalar configurations and also compare with perturbative results
for small couplings, where we focus on a dilatonic coupling function. We
analyze the constraints on the parameters from requiring the curvature
singularity to be located inside the black hole horizon $r_h$ and the relation
to the regularity condition for the scalar field. For scalar field masses $m
r_h \gtrsim 10^{-1}$, this leads to a new and currently most stringent bound on
sGB coupling constant $\alpha$ of $\alpha/r_h^2 \sim 10^{-1}$ in the context of
stellar mass black holes. Lastly, we look at several properties of the black
hole configurations relevant for further work on observational consequences,
including the scalar monopole charge, Arnowitt Deser Misner mass, curvature
invariants and the frequencies of the innermost stable circular orbit and light
ring.
