đi ngủ sớm: to go to sleep at a particularly early hour as around sundown or at sunset.

The campers went to bed with the sun.

Mom goes to bed with the sun, so we can definitely sneak out and go to the party.

When we were young and our parents were busy the household work, we used to go to bed with sun without having dinner.

syms:

go to bed with the chickens: ngủ sớm lúc gà mới lên chuồng

go to bed with the cows: ngủ sớm lúc bò mới vào chuồng

References:

https://idiomation.wordpress.com/2012/03/21/go-to-bed-with-the-chickens-and-get-up-with-the-cows/

https://idioms.thefreedictionary.com/go+to+bed+with+the+sun