How to estimate the analog bandwidth?
If your scope's input amplifier has a frequency response of a first-order RC-filter, you can roughly estimate the bandwidth from the rise time:

$$BW ≈ 0.35 / t_R$$

To clarify, bandwidth is defined by the frequency which is attenuated by -3dB, and the rise time corresponds to the input signal going from 10% to 90% of its amplitude.

Of course, this only applies when you're sure that the observed rise time is due to your scope delaying the signal which originally is (close to) an ideal square wave. If your input signal has a known rise time itself, it should be subtracted from the measured rise time before applying the formula. At 500kHz however, I expect your square wave to be very close to ideal, compared to the rise time you observe with your scope.