"a bit of reflection" is correct and usable in written English.
You can use it to describe a period of thinking about something. For example, "I spent a bit of reflection to come to a decision."
She can afford a bit of reflection from her perch.
And we've had a bit of reflection time, to look at all the stories, and to figure out how to do justice to the last series.
Gentle novelists still jet to tourist spots, hoping a metaphor and a bit of reflection will make up for not quite seeing or understanding anything.
More poetry on the radio is always good, but the lines Feith quotes (e.g. "The thorns you sow will prick your own feet") might have inspired a bit of reflection.
The question of why Ball was so much more effective as "a 16-inch TV image" should, I think, have generated at least a bit of reflection on the peculiar nature of early television comedy, an amazing number of whose stars were performers who, like Ball, worked in an extremely broad style: Skelton, Jackie Gleason, Sid Caesar and (most egregiously) Milton Berle.
Although I like reading books that are relevant to my destination (The God of Small Things in south India; The Sun Also Rises in San Sebastián), I learned last summer that a bit of reflection about back home can be just as pleasurable.
Mr. Gerstner also offered a bit of personal reflection.
Perhaps a bit of further reflection would help.
Here's one last comment from me, which represents a bit of further reflection after re-reading the paper: Press coverage that described this as forecasting a decade of "global cooling" was clearly off the mark, since the global means (as you point out in one of your clarifications) are flat and then rise.
The turning of the calendar into a new year is a time for a bit of nostalgic reflection and ambitious planning for the future.
All in all, at over 100,000 emails, I saw how much people respond to the emails I wrote, and had the time for a bit of personal reflection on how best to optimize this percentage, along with how frequently I'm responding.
