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 $phi_0 gtrsim 5.5times 10^{-3}$, 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.
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