"ask brazenly" is a correct and usable phrase in written English.
It means to ask something boldly or without shame. Example: She always asked for a raise brazenly, even though she knew it was not the right time.
She described how when she became the managing director of Star TV in Hong Kong, she was "stunned at the rush of male executives to form a queue outside my office to brazenly ask for a pay rise".
He or she may even brazenly ask if you "liked that".
He was described as brazenly asking for money from the witness in a text message that read, "Better be 20".
A man leaned out and brazenly asked her whether she would like to join him for coffee.
I approached and brazenly asked for a photograph — I suppose I felt like I had little left to lose in Nashville that afternoon.
"Why am I hanging here anyway?" a Pirate Party poster brazenly asked, the unshaven face in black and white, belonging to the candidate Christopher Lauer, neither smiling nor making the requisite eye contact.
I left and spent a year at Nottingham with Richard Eyre and then Alan Dosser, the artistic director, announced he was taking a sabbatical from the Everyman and I brazenly asked if I could have the job.
And here in Rombek, John Garang, the charismatic leader of the rebel army that concluded a peace agreement with the central government in January, brazenly asked Mr. Zoellick for $30 million.
Then the Tories fired their agency for no good reason, and the next agency did some ads like the spoof ads that had been done with airbrushed Cameron, but with a smiley Gordon apparently admitting the most terrible crimes and then brazenly asking that people nevertheless vote for him.
