I know that it is correct to connect independent clauses using a comma and a coordinating conjunction (for, and, nor, but, or, yet, so) as in "He rides a bike, and she drives a car."
But is it correct to connect 3 independent clauses using only 1 conjunction?
"He rides a bike, she drives a car, and I just walk."
Yes it is correct because the comma implies the conjunction. You actually don't even need the last comma at all, though sometimes it helps to clarify (most common example: let's eat, grandma vs let's eat grandma).
For your example:
He rides a bike, she drives a car, and I just walk.
would be expanded as
He rides a bike and she drives a car and I just walk.
(Note that with the use of the word 'just', 'but' would probably be a better conjunction: 'He rides a bike, she drives a car, but I just walk).
Examples for the other conjunctions:
He neither rides a bike, drives a car, nor walks. ('nor' would take place of the comma).
He wants to ride a bike, drive a car, or walk.
Has he ridden a bike, driven a car or walked yet?
