Higher order Bessel filters ring. You can easily convince yourself of this by looking at the impulse response. The time domain response is the convolution of the signal and impulse response. If the impulse responses goes negative, it must ring. [The situation is the same in DSP for FIR filters, i.e. if a tap is negative, the filter must ring. Well, except for all negative taps, which of course is just a polarity change.]]
The Gaussian never rings.
The Bessel is designed for maximally flat group delay. Now by coincidence, some of the lower order functions don't ring.