Leeds are up to third place after the 3-0 win on Friday night.
Bamford later said, "In the first half I missed two good chances but once the first went in it settled us. The crucial thing was that we didn't give up any part of the game. In general we controlled the game and we played it our way.
"The last time [I was in the Premier League] maybe people said I wasn't ready but I didn't have a proper go at it. It is a fresh start for me to prove I belong here and if i keep on doing it the boys will be happy and I'll be happy.
"We really showed the way Marcelo [Bielsa] wants us to play. Villa are a very good team this year, we knew we had to control the game and we gave away some balls in the first half but in the second half we completely controlled it."
He also remarked: "A dream come true. When the third went in it was elation. A big moment for me.
"It is testament to how the team has worked. Without them I wouldn't be able to score and Marcelo has put a lot of trust in me.
"I wouldn't be able to do it without the team. It was important to bounce back for us.
"I will be telling my kids about this night and I am sure I will never forget it."