Does unity gain Sallen-Key filter fulfill Bessel filter approximation?
The Q for a 2nd order Bessel filter is fixed: 0.577 (or √⅓), what you're showing is for a critically damped 2nd order. However, Bessel filters are lowpass. Frequency transformations may be possible, but all bets are off. If you expect a bandpass to have no overshoot, think again, as a bandpass is not a lowpass: it cancels the DC. If you need clean pulses, then choose a lowpass. Here is the difference between a bandpass and a lowpass in terms of filtering a square wave (both filters chosen for the same fc as the square wave, a bit unusual):