We investigate the imprints of accretion and dynamical friction on the gravitational-wave signals emitted by binary black holes embedded in a scalar dark matter cloud. As a key feature in this work, we focus on scalar fields with a repulsive self-interaction that balances against the self-gravity of the cloud. To a first approximation, the phase of the gravitational-wave signal receives extra correction terms at $-4$PN and $-5.5$PN orders, relative to the prediction of vacuum general relativity, due to accretion and dynamical friction, respectively. Future observations by LISA and B-DECIGO have the potential to detect these effects for a large range of scalar masses~$m_\mathrm{DM}$ and self-interaction couplings~$\lambda_4$; observations by ET and Advanced~LIGO could also detect these effects, albeit in a more limited region of parameter space. Crucially, we find that even if a dark matter cloud has a bulk density~$\rho_0$ that is too dilute to be detected via the effects of dynamical friction, the imprints of accretion could still be observable because it is controlled by the independent scale $\rho_a = 4 m_{\rm DM}^4 c^3/(3 \lambda_4 \hbar^3)$. In the models we consider, the infalling dark matter increases in density up to this characteristic scale $\rho_a$ near the Schwarzschild radius, which sets the accretion rate and its associated impact on the gravitational~waveform.