ABSTRACT Ongoing ground-based radial-velocity observations seeking to detect circumbinary planets focus on single-lined binaries even though over 9 in every 10 binary systems in the solar neighbourhood are double lined. Double-lined binaries are on average brighter, and should in principle yield more precise radial velocities. However, as the two stars orbit one another, they produce a time-varying blending of their weak spectral lines. This makes an accurate measure of radial velocities difficult, producing a typical scatter of $10{\!-\!}15~\rm m\, s^{-1}$. This extra noise prevents the detection of most orbiting circumbinary planets. We develop two new data-driven approaches to disentangle the two stellar components of a double-lined binary, and extract accurate and precise radial velocities. Both approaches use a Gaussian process regression, with the first one working in the spectral domain, whereas the second works on cross-correlated spectra. We apply our new methods to TIC 172900988, a proposed circumbinary system with a double-lined binary, and detect a circumbinary planet with an orbital period of $150~\rm d$, different than previously proposed. We also measure a significant residual scatter, which we speculate is caused by stellar activity. We show that our two data-driven methods outperform the traditionally used TODCOR and TODMOR, for that particular binary system.