After a day spent filming scenes for Help! in London and Twickenham, The Beatles saw an evening performance by Bob Dylan at London's Royal Festival Hall.
After the show they visited Dylan at his suite at the Savoy Hotel. The group were accompanied by singer Alma Cogan, and also present, as Dylan's guest, was beat poet Allen Ginsberg.
The atmosphere was tense at first, until Ginsberg fell into John Lennon's lap from the arm of a sofa. Asked by Ginsberg if he knew William Blake, Lennon replied that he'd never heard of him. His wife Cynthia said: "Oh John, you liar, of course you have!" The exchange broke the ice.
After leaving the Savoy The Beatles spent the rest of the evening nightclubbing in London.

I am confused as to when the Beatles met Dylan.
This (current page) article's headline says "meet"
-- http://www.beatlesbible.com/1965/05/09/the-beatles-meet-bob-dylan/ --
the article says it was 1965 that this occurred
and this other article says "were introduced" in 1964
-- http://www.beatlesbible.com/1964/08/28/bob-dylan-turns-the-beatles-on-to-cannabis/ --
So did they meet in 64 or 65?
You can meet someone on a daily basis. They met him for the first time in 1964.