What are synonyms for taking cover?
Is there a word that means "running to shelter or refuge to save myself from incoming pain or trouble"?
I want to use it in these contexts:
Taking cover time.
Time to take cover.
You have actually mentioned a pretty useful word already --
I think you probably might want to use its verb form.
There is a phrase with the meaning you have asked for
"Make oneself scarce"
As a single word, I would suggest hide or one of it's synonyms which mean taking cover.
However, I also see scram listed as a synonym of "make oneself scarce" which may apply in this case. Scram means "leave abruptly" but when you say "Lets scram" it usually implies trouble is round the corner
Try entrench or barricade with a reflexive pronoun—barricade yourself time. Reflexives don't always sound good in English, but they are used extensively in other languages, like Portuguese.
Why don't you drop the verb take. Call it cover time or bunker time.