The performance of intense Bessel femtosecond pulse propagation in dispersive medium is investigated. Water is chosen as the Kerr medium with large dispersion. We find that within the dispersion length, the temporal profile integrated over the beam radius is controlled mainly by dispersion, whereas the spectral profile is nearly undistorted. We also show the energy flow between different transverse parts of the beam, which provides a reservoir for the intense part of the Bessel beam and extends the nonlinear effect length between the pulse and the Kerr medium as we have previously found in argon.