The new Xin Qiao airport is now open for business and it's 31.8 km from the city center. I took a ride out there today. A straight run (no traffic) to the airport by car took 40 minutes from Hefei. A straight run back to Hefei by shuttle bus also took 40 minutes.
TaxisA taxi will cost about 120 yuan one way (confirmed with a driver). You also have to pay 10 yuan toll to get onto the airport expressway. At the moment, it's not clear how willing Hefei taxi drivers are to go out there. So maybe don't cut it fine with taxis if you're trying to make your flight. At the airport itself, there was a ready supply of taxis to take people back to Hefei.
Buses There are currently 4 shuttle bus lines that run to and from Xin Qiao:
Line 1: Hefei Bus Station (Mingguang Rd) Héféi qìchē zhàn (míngguāng lù) 合肥汽车站(明光路) 06:00-20:30
Line 2: Hefei Car Passenger terminal (Zhanqian Rd) Qìchē kèyùn zǒngzhàn (zhàn qián lù) 汽车客运总站(站前路) 05:40-20:30
Line 3: South Gate Transfer Center (Susong Rd) Nán mén huàn chéng zhōngxīn (sù sōng lù) 南门换乘中心(宿松路)06:00-18:00
Line 4: City Air Terminal (Shouchun Rd) Chéngshì hángzhàn lóu (shòu chūn lù) 城市航站楼 (寿春路) 06:00-19:00
At the airport, the first buses don't begin returning to Hefei until 08:40.

**Note** If the Hefei flight schedule is not convenient, Nanjing airport can also be used as a feeder airport. Hefei railway station to Nanjing south station is about 45 mins/60RMB then at the station transfer to a shuttle bus to Nanjing Lukou airport (20 mins/20 RMB).