The 72-year-old star - who is known for his flamboyant wardrobe - mistook the 'Blowin' in the Wind' hitmaker for his gardener when he arrived as a guest to one of Elton's parties so tried to "make amends" for his gaffe by offering the singer a chance to change out of his "terrible" clothes.
Elton recalled: "Towards the end of the Eighties, I held an insane party in LA, and invited everyone I knew. By mid-evening, I was flying, absolutely out of my mind, when a scruffy-looking guy I didn't recognise wandered into the lit-up garden.
"Who the hell was he? Must be one of the staff, a gardener. I loudly demanded to know what the gardener was doing helping himself to a drink.
"There was a moment's shocked silence, broken by my PA saying, 'Elton, that's not the gardener. It's Bob Dylan.'
"Coked out of my brain and keen to make amends, I rushed over, grabbed him and started steering him towards the house. 'Bob! Bob! We can't have you in those terrible clothes, darling. Come upstairs and I'll fit you out with some of mine at once. Come on, dear!'
"Dylan stared at me, horrified. His expression suggested he was trying hard to think of something he wanted to do less than get dressed up like Elton John, and drawing a blank."
The evening didn't stop Bob from hanging out with Elton, as the 'Tiny Dancer' hitmaker also recalled another evening when he pelted his pal with oranges because he was "so hopeless" at charades, which they were playing with folk duo Paul Simon and Art Garfunkel.
He recalled in an extract from his new autobiography 'Me: Elton John' published in the Daily Mail newspaper:
"Another time, I invited Dylan to dinner with Simon and Garfunkel, and afterwards we played charades.
"At least, they tried to play charades. They were terrible at it. The best thing I can say about Simon and Garfunkel is that they were better than Dylan.
"He couldn't get the hang of the 'How many syllables?' thing at all. He couldn't do 'sounds like' either, come to think of it. One of the best lyricists in the world, the greatest man of letters in the history of rock music, and he couldn't seem to tell you whether a word had one syllable or two syllables or what it rhymed with!
"He was so hopeless, I started throwing oranges at him. Or so I was informed the next morning by a friend.
"That's not really a phone call you want to receive when you're struggling with a hangover. 'Morning, darling -- do you remember throwing oranges at Bob Dylan last night?' Oh God."