* U.S. third-quarter economic growth fastest in three years
* Sterling strengthens on Brexit bill hopes
* Bitcoin hits another all-time high (Updates prices and market activity to U.S. market open; new byline, changes dateline; previous LONDON)
NEW YORK, Nov 29 (Reuters) - The dollar edged higher on Wednesday, adding to this week's gains, as strong U.S. third-quarter economic growth data and signs of progress in U.S. Republicans' efforts to get a tax bill passed helped the currency rebound from recent weakness.
The dollar index, which measures the greenback against six rival currencies, was up 0.1 percent at 93.365. The index, which slipped nearly 1 percent last week, is up 0.6 percent so far this week.
"It's a little bit of an unwind of what we saw last week," said Brad Bechtel, managing director FX at Jefferies in New York.
"We have had some good data, Powell more or less came out as a status quo kind of guy with a with December (rate hike) seemingly a done deal and the tax bill also inched forward a little bit," he said.
On Wednesday, data showed the U.S. economy grew faster than initially thought in the third quarter, notching its quickest pace in three years, as increases in business investment in inventories and equipment offset a moderation in consumer spending.
The dollar has also been supported by remarks on Tuesday by Federal Reserve chair nominee Jerome Powell signaling that the central bank is likely to raise interest rates again next month.
Powell overall presented himself as an extension of the policies set under Fed chair Janet Yellen and her predecessor Ben Bernanke, confirming market expectations that he offered stability despite the change in leadership at the central bank.
The dollar was also on surer footing after Republicans on a Senate panel pushed through a tax-cut bill on Tuesday, setting up a full vote by the Senate as soon as Thursday and advancing President Donald Trump's drive for tax legislation.
"All of these are helping the dollar recover," said Bechtel.
Against the yen the dollar was 0.52 percent higher, as U.S. Treasury yields climbed after the upbeat GDP data.
Bitcoin was the most eye-catching mover, smashing past the $11,000 level for the first time to trade as high as $11,140.49 on the Bitstamp exchange, only hours after it hit the $10,000 mark for the first time.
Britain's sterling jumped to a two-month high on news reports that Britain and the European Union had agreed the outlines of a Brexit settlement bill potentially paving the way to a future trade pact.
Sterling was up 0.54 percent higher at $1.3408.
The Canadian dollar weakened to a nearly four-week low against its U.S. counterpart as oil prices fell. (Reporting by Saqib Iqbal Ahmed; Editing by Frances Kerry)