The Andromeda galaxy (M31) contains a box/peanut bulge (BPB) entangled with a classical bulge (CB) requiring a triaxial modelling to determine the dynamics, stellar and dark matter mass. We construct made-to-measure models fitting new VIRUS-W IFU bulge stellar kinematic observations, the IRAC-3.6µm photometry, and the disc's H I rotation curve. We explore the parameter space for the 3.6µm mass-to-light ratio (Υ 3.6 ), the bar pattern speed (Ω p ), and the dark matter mass in the composite bulge (M B DM ) within 3.2 kpc. Considering Einasto dark matter profiles, we find the best models for Υ 3.6 = 0.72±0.02 M L −1 , M B DM = 1.2 +0.2 −0.4 × 10 10 M and Ω p = 40 ± 5 km s −1 kpc −1 . These models have a dynamical bulge mass of M B dyn =4.25 +0.10 −0.29 ×10 10 M including a stellar mass of M B =3.09 +0.10 −0.12 ×10 10 M (73%), of which the CB has M CB =1.18 +0.06 −0.07 × 10 10 M (28%) and the BPB M BPB =1.91 ± 0.06 × 10 10 M (45%). We also explore models with NFW haloes finding that, while the Einasto models better fit the stellar kinematics, the obtained parameters agree within the errors. The M B DM values agree with adiabatically contracted cosmological NFW haloes with M31's virial mass and radius. The best model has two bulge components with completely different kinematics that only together successfully reproduce the observations (µ 3.6 , υ los , σ los , h3, h4). The modelling includes dust absorption which reproduces the observed kinematic asymmetries. Our results provide new constraints for the early formation of M31 given the lower mass found for the classical bulge and the shallow dark matter profile, as well as the secular evolution of M31 implied by the bar and its resonant interactions with the classical bulge, stellar halo and disc.