Neutron stars (NSs) in low-mass X-ray binaries are considered promising candidate sources of continuous gravitational waves. These NSs are typically rotating many hundreds of times a second. The process of accretion can potentially generate and support non-axisymmetric distortions to the compact object, resulting in persistent emission of gravitational waves. We present a study of existing optical spectroscopic data for Sco X-1, a prime target for continuous gravitational-wave searches, with the aim of providing revised constraints on key orbital parameters required for a directed search with advanced Laser Interferometer Gravitational-Wave Observatory data. From a circular orbit fit to an improved radial velocity curve of the Bowen emission components, we derived an updated orbital period and ephemeris. Centre of symmetry measurements from the Bowen Doppler tomogram yield a centre of the disc component of 90 km s-1, which we interpret as a revised upper limit to the projected orbital velocity of the NS K1. By implementing Monte Carlo binary parameter calculations, and imposing new limits on K1 and the rotational broadening, we obtained a complete set of dynamical system parameter constraints including a new range for K1 of 40-90 km s-1. Finally, we discussed the implications of the updated orbital parameters for future continuous-wave searches.