* Dollar index hits lowest since March 2018

* Euro hits new 2018 high versus dollar

* Bitcoin trades above $35,000

* Graphic: World FX rates in 2021 tmsnrt.rs/2RBWI5E (Adds details, updates prices; changes byline, previous LONDON)

NEW YORK, Jan 6 (Reuters) – The dollar bounced after sinking to its lowest level in nearly three years on Wednesday, with markets anticipating a Democrat win in the U.S. Senate election in Georgia that would clear the path for a larger fiscal stimulus package.

Democrats won one U.S. Senate race in Georgia and led in another on Wednesday, moving closer to a sweep in a deep South state that would give them control of Congress and the power to advance President-elect Joe Biden’s policy goals.

Analysts generally expect a Democrat-controlled Senate would be positive for economic growth globally and thus for most riskier assets, but negative for bonds and the dollar as the U.S. budget and trade deficits swell even further.

As markets priced in the Democrats winning both seats, the dollar index hit its lowest since March 2018 at 89.206, but was last up 0.294% at 89.726.

Fueling expectations of further stimulus measures was a weak report on the labor market in the form of the ADP National Employment Report, which showed private payrolls post their first decline in eight months as coronavirus cases surge.

The dollar also fell to its lowest in six years versus the Swiss franc at 0.87585.

After a fall of nearly 7% in 2020 and dropping as much as 0.9% in the new year, the dollar turned higher as a crowded trade began to unwind. Analysts still expect the longer-term trend for the greenback to be weaker, however.

“Obviously you are going to have to take a little bit of a breather every now and then but we are six days into the new year and the dollar is down roughly half a percent to one percent against G10 currencies, that is a pretty strong move for six days,” said Minh Trang, senior FX trader at Silicon Valley Bank in Santa Clara, California.

“The bearish dollar theme is still in play.”

The euro gave up earlier gains and was down 0.15% to $1.2279, after earlier having risen past major resistance to as high as $1.2349.

Riskier currencies also surged, with the New Zealand dollar and Australian dollar hitting their highest in nearly three years and holding onto most of the gains even as the dollar recovered.

The move was helped by a range of surveys overnight showing that manufacturing globally had proved resilient in December, despite rising virus cases.

Elsewhere, U.S. President Donald Trump escalated tensions with Beijing by signing an executive order banning U.S. transactions with eight Chinese software applications.

After surging on Monday and Tuesday, the yuan softened, after China’s central bank appeared to signal a preference for a more moderate pace of intervention.

The yuan has gained around 10% on the dollar since last May as China’s economic rebound has led the world’s pandemic recovery .

Bitcoin traded above $35,000 for the first time, rising to $35,879.35 in the Asian session and extending a rally that has seen it rise more the 800% since mid-March.

These gains eased somewhat, with the cryptocurrency last up 1.68% at $34,610.52. (Reporting by Chuck Mikolajczak; Editing by Kirsten Donovan)