The phrase "a bit of outrage" is correct and usable in written English.
It can be used to express a small amount of anger or indignation about a particular issue or situation.
Example: "The community expressed a bit of outrage over the proposed changes to the local park."
Alternatives: "a touch of anger" or "a hint of indignation."
After a bit of outrage, Williams apologized.
There was a bit of outrage flying around online recently.
There was, though, a bit of outrage toward the perceived insouciance of Boehner.
She did this with her somber palette, and by loosening the silhouette and using glossy black fur to add a bit of outrage to the hems of wool mini-coats.
It took a little more than 12 hours for Will Ferrell to drop out of a starring role in a satirical film about Ronald Reagan's struggles with Alzheimer's – just long enough for conservatives to muster up a bit of outrage with which to knock the comedian into submission, and to raise questions about whether the free speech brigade has become PC.
Vincent Tan, the Malaysian owner of Cardiff City, has caused a bit of outrage with his new branding for the club.
Need a bit of morning outrage?
A few outspoken members of the financial industry have broken ranks with their more skeptical brethren to say they understand a bit of the outrage of the Occupy Wall Street crowd.
All of this is a bit of an outrage to Valentino Bontempi, an Italian chef who runs his own restaurant on an island in the Moscow River, across a footbridge from the Kremlin.
It was widely noted that Cantona had not really apologised for his actions, and there was a bit of faux outrage at the tone of the Nike publicity celebrating his comeback.
However, I also think we should reserve a bit of our outrage for some of the "victims" of the alleged criminal activity: the institutions of higher education.
