* U.S. third-quarter economic growth fastest in three years
* Sterling strengthens on Brexit bill hopes
* Bitcoin hits another all-time high before giving up gains (Updates prices, market activity; adds comments)
NEW YORK, Nov 29 (Reuters) - The dollar was steady against a basket of currencies on Wednesday, supported by strong U.S. third-quarter economic growth data, but uncertainty surrounding lawmakers efforts to pass a tax bill kept dollar bulls in check.
The dollar index, which measures the greenback against six rival currencies, was at 93.231, little changed on the day.
Congressional Republicans scrambled on Wednesday to reformulate their tax-cut bill to satisfy lawmakers worried about how much it would expand the federal deficit, as the measure moved toward a U.S. Senate floor vote later this week.
The U.S. Senate will vote later Wednesday on whether to begin debate on a Republican tax bill, Senate Majority Leader Mitch McConnell told the chamber.
"There is a lot on the Trump administration's plate in December and their track record is not the best," said Alfonso Esparza, senior currency analyst at OANDA in Toronto.
"Until something is delivered the market is a bit hesitant."
The dollar index, which slipped nearly 1 percent last week, is up 0.5 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.
The greenback has drawn support from strong data and remarks on Tuesday by Federal Reserve chair nominee Jerome Powell signaling that the central bank is likely to raise interest rates again next month, Bechtel said.
Data on Wednesday 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.
Against the yen the dollar was 0.36 percent higher, as U.S. Treasury yields climbed after the upbeat GDP data.
Bitcoin was the most eye-catching mover, and zoomed past $11,000 to hit a record high of $11,395 before pulling back to trade at $9,919.58, little changed on the day.
Sterling rose to a two-month high after European Union diplomats said that Britain has moved "close" to EU demands over Brexit, although concerns that differences remain on key conditions capped the currency's gains on Wednesday.
Sterling was 0.59 percent higher at $1.3415.
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 and Lisa Shumaker)