  The deformability of a compact object under the presence of a tidal
perturbation is encoded in the tidal Love numbers (TLNs), which vanish for
isolated black holes in vacuum. We show that the TLNs of black holes surrounded
by matter fields do not vanish and can be used to probe the environment around
binary black holes. In particular, we compute the TLNs for the case of a black
hole surrounded by a scalar condensate under the presence of scalar and vector
tidal perturbations, finding a strong power-law behavior of the TLN in terms of
the mass of the scalar field. Using this result as a proxy for gravitational
tidal perturbations, we show that future gravitational-wave detectors like the
Einstein Telescope and LISA can impose stringent constraints on the mass of
ultralight bosons that condensate around black holes due to accretion or
superradiance. Interestingly, LISA could measure the tidal deformability of
dressed black holes across the range from stellar-mass ($\approx 10^2 M_\odot$)
to supermassive ($\approx 10^7 M_\odot$) objects, providing a measurement of
the mass of ultralight bosons in the range $(10^{-17} - 10^{-13}) \, {\rm eV}$
with less than $10\%$ accuracy, thus filling the gap between other
superradiance-driven constraints coming from terrestrial and space
interferometers. Altogether, LISA and Einstein Telescope can probe tidal
effects from dressed black holes in the combined mass range $(10^{-17} -
10^{-11}) \, {\rm eV}$.
