  We show how gravitational-wave observations of binary black hole (BBH)
mergers can constrain the physical characteristics of a scalar field cloud
parameterized by mass $\tilde{\mu}$ and strength $\phi_0$ that may surround
them. We numerically study the inspiraling equal-mass, non-spinning BBH systems
dressed in such clouds, focusing especially on the gravitational-wave signals
emitted by their merger-ringdown phase. These waveforms clearly reveal that
larger values of $\tilde{\mu}$ or $\phi_0$ cause bigger changes in the
amplitude and frequency of the scalar-field-BBH ringdown signals. We show that
the numerical waveforms of scalar-field-BBHs can be modelled as chirping
sine-Gaussians, with matches in excess of 95%. This observation enables one to
employ computationally expensive Bayesian studies for estimating the parameters
of such binaries. Using our chirping sine-Gaussian signal model we establish
that observations of BBH mergers at a distance of 450 Mpc will allow to
distinguish BBHs without any scalar field from those with a field strength
$\phi_0 \gtrsim 5.5\times 10^{-3}$, at any fixed value of $\tilde \mu \in
[0.3,0.8]$, with 90% confidence or better, in single detectors with Advanced
LIGO/Virgo type sensitivities. This provides hope for the possibility of
determining or constraining the mass of ultra-light bosons with
gravitational-wave observations of BBH mergers.
