FOREX-Dollar dips on shutdown worries, bitcoin clears $10,000

* Worries over U.S. government shutdown grow

* Bitcoin hits another all-time high

* Sterling strengthens on Brexit bill hopes

* N.Korea missile launch leaves little impact for now

* Graphic: World FX rates in 2017 http://tmsnrt.rs/2egbfVh

LONDON, Nov 29 (Reuters) - The dollar dipped against a basket of currencies on Wednesday, pulled down by broad strength in sterling as well as worries over a possible U.S. government shutdown after Democrats pulled out of a meeting with President Donald Trump.

Bitcoin was once again the most eye-catching mover, smashing past the $10,000 level for the first time to trade as high as $10,753 on the Bitstamp exchange after a more than elevenfold increase in value since the start of the year.

The dollar, already on track for its worst month since July and its worst year since 2003, dipped 0.2 percent against its currency basket.

Democratic leaders in U.S. Congress on Tuesday skipped a meeting with Trump that was to have focused on the budget, after a tweet Trump sent earlier in the day attacking them as weak on illegal immigration and bent on raising taxes.

That raised the risk of a government shutdown ahead of the Dec. 8 deadline, with both sides far apart on the terms of an agreement.

"More attention is being given by markets...to this potential shutdown on December 8th and the fact that we had this tweet from Trump yesterday," said MUFG macro strategist Derek Halpenny, in London.

Jerome Powell, Trump's choice to lead the U.S. Federal Reserve, made little mention of monetary policy in a controversy-free hearing on his nomination to take over the central bank on Tuesday.

"Powell didnt rock the boat in any major way...but theres enough debate going on in the FOMC (Federal Open Market Committee) in terms of whats behind low inflation to prompt a period of pause (in rate hikes) in the first half of next year," Halpenny said.

He added that Britain's pound, which jumped late on Tuesday on hopes that Britain would reach a divorce bill deal with the European Union and extended gains on Wednesday, was helping to drag down the dollar across the board. GBP/ 3/8

The euro climbed 0.3 percent to $1.1882.

Data on Tuesday showed U.S consumer confidence surged to a near 17-year high in November, driven by a robust labour market, giving the dollar a temporary boost.

The currency market appeared unaffected by a North Korean test launch of what appeared to be an intercontinental ballistic missile (ICBM) that landed close to Japan. It was North Korea's first test launch since mid-September.

"The market appears to have gotten used to such events. How the United States responds, however, still bears watching," said Shin Kadota, senior strategist at Barclays in Tokyo.

(Reporting by Jemima Kelly; Editing by Keith Weir)