  Ultralight bosons are possible fundamental building blocks of nature, and
promising dark matter candidates. They can trigger superradiant instabilities
of spinning black holes (BHs) and form long-lived "bosonic clouds" that slowly
dissipate energy through the emission of gravitational waves (GWs). Previous
studies constrained ultralight bosons by searching for the stochastic
gravitational wave background (SGWB) emitted by these sources in LIGO data,
focusing on the most unstable dipolar and quadrupolar modes. Here we focus on
scalar bosons and extend previous works by: (i) studying in detail the impact
of higher modes in the SGWB; (ii) exploring the potential of future proposed
ground-based GW detectors, such as the Neutron Star Extreme Matter Observatory,
the Einstein Telescope and Cosmic Explorer, to detect this SGWB. We find that
higher modes largely dominate the SGWB for bosons with masses $\gtrsim
10^{-12}$ eV, which is particularly relevant for future GW detectors. By
estimating the signal-to-noise ratio of this SGWB, due to both stellar-origin
BHs and from a hypothetical population of primordial BHs, we find that future
ground-based GW detectors could observe or constrain bosons in the mass range
$\sim [7\times 10^{-14}, 2\times 10^{-11}]$ eV and significantly improve on
current and future constraints imposed by LIGO and Virgo observations.
