Answer:
Bilbo's luck should be seen as a plot device that reinforces the theme of Bilbo's growing self-awareness and self-confidence. Bilbo( Baggins) was so scared, while trying to say "more time" he ended up saying "time" and that luckily was the answer.
It becomes the factor of the plot because they always escape from things that capture them and how they get saved by Bilbo and his ring.
hope this helps!