"regularly ask" is grammatically correct and can be used in written English.
It means to ask on a regular or frequent basis. Example: The teacher regularly asks her students to hand in their homework on time.
Regularly ask yourself: What's your job, knucklehead?
"I regularly ask myself what happened," he said.
Some people regularly ask us why we request permissions; this is completely understandable, sensible even.
Regularly ask them, "What do you think about X?" and take them into your confidence.
Readers regularly ask me when I will throw in the towel on Iraq.
Pollsters regularly ask people whether they feel English only, English and British, or just British.
Airport workers regularly ask her to book fewer people on some flights.
Moreover, she said, "My nonartist friends regularly ask me if I'm pounding the pavement looking for another 'real' job".
I am a third-generation Mexican-American, and European-Americans regularly ask me how long I've been in this country.
It's highly unlikely that corporate bosses regularly ask themselves if their businesses have a right to exist.
He seems to regularly ask himself the question "What is Chanel?" — as if he knows it's a living thing.
