I doo not transport fish in buckets in a car. They get sloshed around and may get banged into the hard side of the bucket. I have been shipping and transporting fish for many years. I use bagsm styros and never use oxygen. I breed a and sell some very expensive plecos. So losing fish to poor packing is not an option.
As for blowing into a bag -->
from Wiki
I do this when the time in the bag is 12 hours or less. When I ship, I use an
air pump to inflate the bag. The key to packing is in five things:
1. No matter what position the bag is in the fish must be able to stay submerged.
2. The width of the bag must be greater than the length of the fish going into it.
3. There must be at least 50% air or more if as long as it meets condition #1.
4. The bag must be knotted and/or rubber banded to seal it to the greatest possible extent.
5. The basgs must not easily moce arounf in a bpx. Add padding material to prevent this and to se the bags in place. Even crumpled newspaper works.
Also, when shipping I normally add a small piece of Poly-Filter to the bag.
https://www.poly-bio-marine.com/
I have shipped fish get delayed and take over 4 days to arrive and all the fish were alive.