The Mystics (12-7) defeated the Lost Angeles Sparks on Saturday 83-74 before dropping a 97-91 decision to the Seattle Storm on Sunday.
Washington led 56-48 in the third quarter at Seattle before the Storm went on a 27-10 run over the final seven minutes to lead 75-66 at the start of the fourth and held off a late Mystics rally.
"Yeah, once you get the first one you get greedy and want the second one," Mystics coach Mike Thibault said of the road swing. "We gave ourselves a chance at the start. We had a good start and when you play a back-to-back, you always wonder how you're going to start, but the third quarter was like an avalanche for about four or five minutes."
"We have to go home and get rested because we have a big week ahead of us," Thibault said after Sunday's game.
The Mystics face the third-place Dream (9-9) in a home-and-home twice this week sandwiched around a visit from the fourth-place Chicago Sky. Washington and Atlanta will be meeting for the first time this season.
Delle Donne was named Eastern Conference Player of the Week. She averaged 20.3 points over three games, along with 5.7 rebounds. She shot 45.1 percent from the field to earn the 15th Player of the Week nod of her six-year career.
Atlanta is coming off a big win, 76-70 over the visiting Phoenix Mercury on Sunday. The Dream scored the first nine points and led by as many as 23 points late in the third quarter before holding off a Phoenix surge.
Wednesday's game marks the return of guard Alex Bentley to the Dream. Bentley was acquired Monday from the Connecticut Sun for Layshia Clarendon and a 2019 second-round WNBA Draft pick.
Bentley, who was drafted by Atlanta and played for the Dream in 2013, was averaging 10 points, 3.2 assists and 1.4 rebounds for the Sun. She has a career average of 11.0 points and has knocked down long distance shots at a 30.8 percent clip.
Dream coach Nicki Collen was an assistant with the Sun from 2015-17.
"Having had the opportunity to coach Alex Bentley in Connecticut for two seasons, I know she can be a dynamic scorer, but more importantly, she can create opportunities for her teammates because of her speed and skill with the basketball," Collen told the Atlanta Journal Constitution.
Washington won all three meetings last season.