The saying is:
Time flies like an arrow; Fruit flies like a banana.
Which, from the title, is an example of:
A garden path sentence — "a grammatically correct sentence that starts in such a way that a reader's most likely interpretation will be incorrect". On top of that, the title is doubly thematic since the saying is about time flying ("hurry up") and flies/bananas ("the garden path").
Because:
Flowing unceasingly; => Time (philosophically)
Eaters of dung; => flies (of the insect variety)
A sort of affection; => like (to be fond of someone)
Almost a quarter past one; => an (1:14 is almost 1:15, which via A1-Z26 gives AN)
Take a bow for this. => arrow (as in bow and arrow)
Found with vegetables; => Fruit (as in fruit and veg)
On the front of trousers; => flies (of the zipper variety)
Done on Facebook; => like (👍)
One and only one; => a (singular article)
Made up half of ones. => banana (half "a"s)