The isolation, simple apparent structure and low luminosity of the nearby spiral galaxy NGC 6503 make it an ideal candidate for an in-depth kinematic and photometric study. We introduce a new publicly available code, DiskFit, that implements procedures for fitting non-axisymmetries in either kinematic or photometric data. We use DiskFit to analyse new Hα and CO velocity field data as well as H i kinematics from Greisen et al. to search for non-circular motions in the disc of NGC 6503. We find NGC 6503 to have remarkably regular gas kinematics that are well described by rotation only. We also use DiskFit and a new Ks-band image of NGC 6503 to constrain photometric models of the disc, bar and bulge. We find the galaxy to be photometrically dominated by the disc. We find NGC 6503 to contain a faint bar and an exponential bulge which together contribute only ∼5 per cent of the total galaxy light. The combination of our kinematic and photometric DiskFit models suggests that NGC 6503 contains a weak, end-on bar that may have produced its Type II surface brightness profile but is unlikely to be responsible for its strong σ-drop.