The short answer for a spiny bottom-dweller
A corydoras catfish travels best in an extra-thick double bag of its own tank water, laid flat inside a dark, insulated box. Two features of this species shape the whole method. Its pectoral and dorsal fin spines lock stiff when it is frightened, and those spines can pierce a single thin bag during a long journey. It also lives on the bottom, so a flat bag gives the school a wide floor to rest on instead of piling the fish into a corner of an upright bag. Keep the group together, keep it dark, and keep the temperature steady.
Preparing a cory school for the road
Fasting the school for a day before departure is the preparation a corydoras group needs most. These catfish scavenge constantly, and a full stomach in a sealed bag means waste building in water nothing is filtering. Catch them with patience: lower a wide soft net or container and herd gently, because a chased corydoras thrashes and raises its spines, which is exactly how injuries and punctured bags happen. Work when the fish are calm, and bag the whole school in one or two generous bags rather than separating individuals, since a corydoras alone in transit is a frightened fish.
Bagging so spines cannot drain the water
Double-bagging with the thickest bags you have is non-negotiable for corydoras on a long journey. Fill the inner bag about one-third with tank water, add the fish, fill the rest with air or oxygen, and tie it off. Slide it into the second bag tied from the opposite end, so the sealed corners face different directions and one spine prick cannot empty both layers. Lay the finished bag flat in the insulated box on a cushioning layer, with soft packing around it so it cannot slide. Keep the box level and out of direct heat or cold, and place nothing heavy on top that could press the bag.
What corydoras do during a long journey
An occasional sudden dart to the surface is normal corydoras behaviour, not a sign of trouble. This species supplements its breathing by gulping air at the surface, at home and in a travel bag alike, which is one reason the air space above the water matters. Between those darts, a healthy travelling school settles together on the bag's floor in the dark. Resist opening the box to count them, because light and movement trigger the stiff-spined panic response you are trying to avoid. Keep the box still during stops, carry it in both hands, and never leave it in a vehicle that will bake or freeze while parked.
Release and the first day after arrival
Floating the flat bag in the destination tank warms or cools the corydoras gradually before any water mixes. Open the bag only once temperatures feel equal, add tank water in small stages, then tip the school out gently rather than netting them a second time. Provide dim light and somewhere to shelter, and offer a small sinking meal once they are nosing around the substrate again. Watch for torn fins, red patches around the barbels, or a fish resting tilted and apart from the group, and ask an aquatic veterinarian for guidance if those signs appear or appetite does not return. Noting the school's usual foods, group size, and water readings in a KinsLe Pet Passport lets the person at the far end release them into conditions that feel familiar.