Phase-resolved VLT spectroscopy of the bursting Low Mass X-ray Binaries 4U 1636-536/V801 Ara and 4U 1735-444/V926 Sco is presented . Doppler images of the NIII \lambda 4640 Bowen transition reveal compact spots which we attribute to fluorescent emission from the donor star and enable us to define a new set of spectroscopic ephemerides . We measure K _ { em } = 277 \pm 22 km s ^ { -1 } and K _ { em } = 226 \pm 22 km s ^ { -1 } from the NIII spots in V801 Ara and V926 Sco respectively which represent strict lower limits to the radial velocity semi-amplitude of the donor stars . Our new ephemerides provide confirmation that lightcurve maxima in V801 Ara and likely V926 Sco occur at superior conjunction of the donor star and hence photometric modulation is caused by the visibility of the X-ray heated donor . The velocities of HeII \lambda 4686 and the broad Bowen blend are strongly modulated with the orbital period , with phasing supporting emission dominated by the disc bulge . In addition , a reanalysis of burst oscillations in V801 Ara , using our spectroscopic T _ { 0 } , leads to K _ { 1 } = 90 - 113 km s ^ { -1 } . We also estimate the K - corrections for all possible disc flaring angles and present the first dynamical constraints on the masses of these X-ray bursters . These are K _ { 2 } = 360 \pm 74 km s ^ { -1 } , f ( M ) = 0.76 \pm 0.47 M _ { \odot } and q = 0.21 - 0.34 for V801 Ara and K _ { 2 } = 298 \pm 83 km s ^ { -1 } , f ( M ) = 0.53 \pm 0.44 M _ { \odot } and q = 0.05 - 0.41 for V926 Sco . Disc flaring angles \alpha \geq 12 ^ { \circ } and q \simeq 0.26 - 0.34 are favoured for V801 Ara whereas the lack of K _ { 1 } constraint for V926 Sco prevents tight constraints on this system . Although both binaries seem to have intermediate inclinations , the larger equivalent width of the narrrow NIII line in V801 Ara at phase 0.5 relative to phase 0 suggests that it has the higher inclination of the two .