The phrase "fitting to ask" is correct and usable in written English.
It is used to indicate that a certain question or inquiry is appropriate or relevant given a particular situation or context. For example, "Given the circumstances, it seems fitting to ask whether you plan to extend your stay."
Since Thanksgiving signifies the memory of a feast between a group of our continent's original inhabitants and some recent arrivals from Europe, and since corn is such an elementally American food, it seemed fitting to ask Mr. Katz whether he'd be willing to share the recipe with Times readers.
On the 150th anniversary of the Emancipation Proclamation, it is fitting to ask for a progress report.
So at the play's recent opening night, it seemed fitting to ask the celebrity audience, some of Broadway's finest, what creative outlet they had when they were kids.
"As Nickelodeon Studios is based in New York, I felt it fitting to ask the Big Apple to show its love for Stephen by embracing SpongeBob's classic yellow glow," fan Alison P. said in her petition on the Care2 website.
So it's fitting to ask, what is it about this ball-and-stick game that is so deeply embedded in our culture -- with influence well beyond the actual sport of baseball?
Since our government representatives and the nation as a whole are so focused on the deficit and the national debt to the point of reducing funding for a number of important domestic programs, it seems fitting to ask whether these expenditures for military action in Libya, are warranted.
David Westin, the ABC News president, said he did not see fit to ask for more time from the ABC network headquarters in Burbank, Calif.
It is also possible that one of the moderators might see fit to ask one of Mr. Romney's rivals whether they think a discussion about Mormonism distracts from the important economic issues facing the country.
"Despite all the public questioning and statements of concern by us and others, and our freedom-of-information requests, and the extensive press coverage the FBI's Baltimore flights received, the Baltimore police did not see fit to ask the public's permission to use this startling new technology on the city's population," he said.
Only an Independent Counsel has the power to compel testimony -- any testimony they see fit to ask.
