The most common and most likely answer to this crossword clue is the 5 plus 3 letter word JIFFY BAG
I've seen this crossword clue in The Daily Telegraph
J
I
F
F
Y
B
A
G
Buddy explains!
The straight part
We know that "well-padded means of transport" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case well-padded means of transport = jiffy bag.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.