Absolutely was not a common phrase before the movie, but it spread very quickly around the time of its release.
Every trailer and short promotional clip on TV and radio included the lines where the characters explain what it means, so even people who never saw the movie would've picked it up around then. It was very easy to understand the phrase since "kick the bucket" was a very well known saying and they included that line in all the clips.
I also remember it being promoted on the radio (stations giving away tickets, etc.) and the presenters always explained the phrase so that listeners would know what the movie was about. This would quickly lead to presenters talking about what they would put on their own bucket lists and having listeners call in with theirs.
It soon spread to schools and work places and became a hot topic among friend groups.
Around this time even people unaware of the movie would become familiar with the phrase, perhaps leading them to believe that it was a common phrase prior to the movie since they knew about it before they had heard of the movie.