We present analytical expressions for the frequency bandwidth of gain of broadside-beam metasurface (MTS) antennas. These antennas are based on a transformation between a cylindrical surface-wave (SW) and a leaky-wave through interaction with a periodically modulated MTS. The latter is realized by using subwavelength patches of different dimensions printed on a grounded slab. We demonstrate that, for an appropriate choice of the modulation index, the relative bandwidth is inversely proportional to the antenna radius in terms of a wavelength, by a coefficient which is directly proportional to the group velocity at the central frequency of the SW supported by the average impedance. It is seen, therefore that the product bandwidth-gain is linearly proportional by means of the same coefficients to the antenna radius in wavelengths. The simple formulas introduced in the paper have been thoroughly tested through an accurate analysis.