After a narrow defeat to Germany and heavy loss to Germany, Bywater admitted he and his team-mates needed to show their character.
And a 71-55 win over Japan in their final group game is a third straight win and books a quarter-final against either Spain, Turkey or the USA.
"It was another bulldog performance and that was a phenomenal basketball,” said Bywater, who contributed 15 points.
"I feel I'm peaking at the right time after a tough year with injury. It's not about me though, it's about the team performance.
"We had a tough start but we've taken two defeats on the chin but bounced back and showed our character. Other teams might have slumped but we've emerged stronger for it.
“We need to keep this momentum going and confidence is sky high right now. This is the closest knit team we've had and that is making a difference.
“We've got more strength in depth than any team in this tournament. This is a long tournament and we've got the ability to rest people and give other players time on court, which is making a difference.
"There are eight teams in this tournament that could medal here, so whoever we play in the quarter-final is going to be tough.
"And whoever it is will struggle if we play as well as we did against Japan."
Coach Murray Treseder was delighted with the dominant display against Japan, even if a worried about a lapse in concentration late in the match when the victory was already assured.
Britain have won bronze at the last two Games and Treseder remains confident of an upgrade - although he concedes it will be tough.
"I thought we were good for three quarters of the match but then we slowed down a little bit and I wasn't happy,” he said.
"If we play like that against the standards of team we'll now play that will cost us the match.
"However, the last three games have been of an extraordinary hight standard and it's setting us up for a really brutal quarter-final, whoever we play.
"The last three games have been very good, although with due respect to those three teams whoever we play next will be a step up in competition.
"After that second loss we asked for a response and what we've been given by the team has been wonderful.
"It sets us up nicely but we're under no illusions how tough it's going to be."
Meanwhile, Garry Peel's women's side lost 67-50 to a world-class Canada team in their final group but it was a much improved performance as they prepare to take on Germany in the quarter-finals.
However, Peel admits his young side have felt the pressure of their home Games, with capacity crowds at the North Greenwich Arena both an advantage and disadvantage.
But after booking progress to the knockout stages he believes the pressure is off.
"The girls were so frightened and tense at the start of the tournament and it shocked them and me how much it affected them," he said.
"Now we're a bit more relaxed and into the tournament and it's getting easier.
"It was a good performance. Some of the girls have been a bit nervous in the opening games and it's showed but they are starting to relax now.
"We know we can beat Germany. We've achieved our goal to qualify for the quarter-finals.
"The pressure is off us a little bit now. Our overall goal is still top four and if we start against Germany how we did against Canada then we will rattle them.
"I think we're better than the record suggests. It's a young team and this is a building experience for us.
"However, other teams are still frightened of us because they know we can produce a big game."