There doesn't seem to be an official rule set that has been adopted universally, but some of the clubs in my area are using this one published on 3-gun Nation website h ttp://3gunnation.com/rules
Under transporting firearms section is:
1.7 TRANSPORTING FIREARMS: (To and from vehicles or between stages)
1.7.1 Pistols must be transported from vehicles or between stages cased with a chamber safety flag or remain
holstered.
1.7.2 Rifles, Carbines & Shotguns must be transported with the bolt closed on a chamber safety flag, detachable
magazines must be removed, tubes unloaded.
1.7.3 Rifles, Carbines & Shotguns must be cased OR if hand carried or slung, the muzzle must be pointed up.
1.7.3.1 Using a cart where the muzzles are pointed downward is allowed.
Note 1: The ONLY time a shotgun or rifle may not have a chamber safety flag inserted is after the “Make Ready”
command or in a Safe Area.