The phrase "abandon a bit" is correct and usable in written English.
It can be used when suggesting to let go of something temporarily or to not focus on a minor detail.
Example: "In order to move forward with the project, we may need to abandon a bit of our original plan."
Alternatives: "let go of a little" or "set aside a small part".
At the same time we were so excited about going down this new direction with DJ Hero, I think we abandoned a bit of the innovation that was required in the Guitar Hero franchise.
"Cemeteries become vibrant places then, where you can meet people, not these places that are a little bit abandoned, a little bit sad and lonely and neglected.
He said the vehicle "reeked of gunpowder" and seemed oddly abandoned — "a little bit more than just a parked car with a cigarette in the ashtray".
The expected instructions from an exploration manager, to stop drilling and abandon a well where the bit hits the Precambrian basement, no longer applies.
This flourish — one that the chain is, alas, abandoning — is a bit like watching salad and dressing being forcibly introduced like two families at a boozy shotgun wedding.
But there ingenuity ran out, and after a few years of struggle it was abandoned as a bit of an embarrassing mistake.
He made several unsuccessful passes at the project before he remembered a number he had abandoned two decades earlier: a bit of purplish patriotic verse, set to a rousing tune, originally written in 1918 for his World War I-themed revue, "Yip Yip Yaphank".
It requires a bit more nuance these days and viewers are quicker to pick up or abandon a series.
Dimly Lit Window in an Otherwise Abandoned Home is a bit too long and also quite threatening.
After some snatched moments on the web I stumbled across Hilton's Relaxation Rooms - specifically designed to make you sleep; rooms with whole 'zones' dedicated to abandoning yourself to a bit of shuteye.
