  Accreting neutron stars (NS) can exhibit high frequency modulations in their
lightcurves during thermonuclear X-ray bursts, known as burst oscillations.
These frequencies can be offset from the NS spin frequency by several Hz (where
known independently) and can drift by 1-3 Hz. One plausible explanation is that
a wave is present in the bursting ocean, the rotating frame frequency of which
is the offset. The frequency of the wave should decrease (in the rotating
frame) as the burst cools hence explaining the drift. A strong candidate is a
buoyant $r$-mode. To date, models that calculated the frequency of this mode
taking into account the radial structure neglected relativistic effects and
predicted rotating frame frequencies of $\sim$ 4 Hz and frequency drifts of > 5
Hz; too large to be consistent with observations. We present a calculation that
includes frame-dragging and gravitational redshift that reduces the rotating
frame frequency by up to 30 % and frequency drift by up to 20 %. Updating
previous models for the ocean cooling in the aftermath of the burst to a model
more representative of detailed calculations of thermonuclear X-ray bursts
reduces the frequency of the mode still further. This model, combined with
relativistic effects, can reduce the rotating frequency of the mode to $\sim$ 2
Hz and frequency drift to $\sim$ 2 Hz, which is closer to the observed values.
