I’m not sure if there is a specific command just for checking bridge connectivity.
I came across this this thread that may be helpful. The UseBridges 1 option in your torcc makes sure Tor only connects to bridges.
Whonix forum:
https://forums.whonix.org/t/how-can-i-check-if-tor-is-connected-through-a-bridge-in-arm/2794
I hope this helps.