The passive HPF has no effect on initial response time (to a step function from the sensor). The LPF is first order, and so it reaches 63% of its ultimate (gain=101) value in 68 msec. (which is 680K x 100nF). But by this time the HPF is starting to fall off too, so it starts heading back toward zero with a time constant of 220 msec, so the output of the amplifier never does reach its gain=101 value. Calculating what the response time is for this circuit depends on how you want to define the response time. Normally for a first order system, the response time is the time to reach 63% of the eventual steady-state value. But since this circuit never does reach the 100% value, the meaning of the 63% point is somewhat ambiguous.