Using a 5 gallon painter's bucket with 3 gallons of water and slits in the top is much much better than bagging it.
If you are driving to school, there is no reason I can see to bag it.
Make sure the bucket is well sealed/well ventilated, and NO LR WITH THE FISH!!! Sliding rocks or corals could injure/kill the fish and/or coral.
Good luck.
BTW, is this a college class??