The phrase "a bit more quickly" is correct and usable in written English.
It can be used when you want to indicate a slight increase in speed or urgency in an action or process.
Example: "If we could finish this project a bit more quickly, we would meet the deadline."
Alternatives: "a little faster" or "somewhat more rapidly".
But presidential politics appears to have moved the process along a bit more quickly than usual.
Likewise, a bee may waggle a bit more quickly to indicate greater distance.
The United States will grow as well, a bit more quickly than Indonesia but not a boom like India's.
Kids grow up, in fiction and in life, and it is true that they tend to grow up a bit more quickly in life than they do in our fiction.
His country-club pals are overwhelmingly industrialists, many of whom have long pushed for a weaker dollar.For the politicos at the White House, too, a dollar that slides a bit more quickly has its attractions.
Some of those little-known firms, such as Renesas Electronics, whose tiny microcontrollers are vital for the car industry, are recovering fast which will help the wheels of the global economy spin a bit more quickly.
"It's a way to do what we otherwise could do, but do it a little bit more quickly".
Maybe a little bit more quickly.
I wonder if we're conditioned to believe in the capabilities of men in this role a little bit more quickly than with women".
Brzezinski is compellingly logical -- and his commentary implies disappointment in the current president and his team for not taking the bit more quickly and decisively.
It won't be easy, not when you still have several dominant characters on board who are used to winning trophies playing a certain way; not when the new signings are unfamiliar with the particular demands of the Premier League where everything happens more quickly with a bit more force.
