The squad had initially paused discussions ahead of the Women's World Cup, where England finished runners-up after losing the final to Spain.
"We've come to an agreement," Bright, who is standing in for the injured Leah Williamson, told reporters ahead of Friday's Nations League game against Scotland.
"We've had a really good conversation with the FA and expressed that we want to be world leaders both on and off the pitch.
"That conversation was needed and the conversations will be ongoing between the leadership team and the FA. We're really positive that, moving forward, things will be different. Overall it was very good."
The players were locked in a dispute with the FA after the announcement that the world governing body FIFA would directly pay individual fees to players at the World Cup starting at $30,000 and rising to $270,000 for each member of the winning team.
But the FA's decision not to offer the England team bonus payments on top of the fees they will earn from FIFA had been a bone of contention in the build-up to the tournament.
Reuters has contacted the FA for comment.
PAY ISSUES
The Professional Footballers' Association (PFA) had said in July that issues surrounding pay were especially apparent in countries where players did not have collective bargaining agreements.
FIFA had announced a financial contribution specifically earmarked for all World Cup players, which meant the allocation per England squad member was $195,000 as they were runners-up.
Spain's soccer federation was also set to receive $4.29 million, with the English FA taking home a little over $3 million as part of FIFA's record distribution.
Bright said the discussions with the FA were "bigger than just the bonus".
"The women's game is evolving very quickly and conversations like this need to happen in order to make sure that, in all areas, we're at the top of our game.
"As players, we feel really confident moving forward with the structure we now have in place."
England manager Sarina Wiegman said she was expecting the agreement and looked forward to turning attention back to football.
"The conversations had been going really well but the World Cup was ahead of us, so they needed to stop and then start up after the World Cup," she said.
"They didn't come to an agreement then but the connections were made and there was communication all the time. Now this is solved, we move forward and it looks really good."
