  Inflationary cosmology with a preceding nonsingular bounce can lead to
changes on the primordial density fluctuations. One significant prediction is
that the amplitude of the power spectrum may undergo a jump at a critical
scale. In this Letter we propose a phenomenological parametrization of the
primordial power spectrum in this scenario and confront the jump feature with
latest cosmological data. Performing a global fitting, we utilize this
possibility to derive a novel method for constraining bounce parameters via
cosmological measurements. Combining the CMB, LSS and SNIa data, our result
interestingly reveals that a nonsingular bounce, if exists, should be a fast
bounce which happens at a very high energy scale, as we get an upper limit on
the bounce parameters.
