If your only source is the movies, one of the annoying gripes about them is they have this deceptive editing that makes it seem like Frodo left the Shire within a relatively short timespan after the birthday party.
Frodo got the ring on the 22nd of September of 3001. He leaves Bag End on the 23rd of September...of 3018.

I like this template so much better than the Spider-Man one that people constantly use backwards.