AstroSat has surveyed M31 with the UVIT telescope during 2017 to 2019. The central bulge of M31 was observed in 2750-2850 A, 2000-2400 A, 1600-1850 A, 1450-1750 A, and 1200-1800 A filters. A radial profile analysis, averaged along elliptical contours which approximate the bulge shape, was carried out in each filter. The profiles follow a Sersic function with an excess for the inner 8" in all filters, or can be fit with two Sersic functions (including the excess). The ultraviolet colours of the bulge are found to change systematically with radius, with the center of the bulge bluer (hotter). We fit the UVIT spectral energy distributions (SEDs) for the whole bulge and for 10 elliptical annuli with single stellar population (SSP) models. A combination of two SSPs fits the UVIT SEDs much better than one SSP, and three SSPs fits the data best. The properties of the three SSPs are age, metallicity (Z) and mass of each SSP. The best fit model is a dominant old, metal-poor (10^10 yr, log(Z/Zsun)=-2, with Zsun the solar metallicity) population plus a 15% contribution from an intermediate (10^9.5 yr, log(Z/Zsun)=-2) population plus a small contribution (2%) from a young high-metallicity (10^8.5 yr, log(Z/Zsun)=-0.5) population. The results are consistent with previous studies of M31 in optical: both reveal an active merger history for M31.