  Galactic binaries with orbital periods less than 1 hour are strong
gravitational wave sources in the mHz regime, ideal for the Laser
Interferometer Space Antenna (LISA). At least several hundred, maybe up to a
thousand of those binaries are predicted to be sufficiently bright in
electromagnetic wavebands to allow detection in both the electromagnetic and
the gravitational bands allowing us to perform multi-messenger studies on a
statistically significant sample. Theory predicts that a large number of these
sources will be located in the Galactic Plane and in particular towards the
Galactic Bulge region. Some of these tight binaries may host sub-stellar
tertiaries. In this white paper we propose an observing strategy for the
Galactic Bulge Time Domain Survey which would use the unique observing
capabilities of the Nancy Grace Roman Space telescope to discover and study
several 10s of new strong LISA gravitational sources as well as exoplanet
candidates around compact white dwarf binaries and other short period variables
such as flaring stars, compact pulsators and rotators.
