Dean Smith's men had won all of their first four Premier League games going into the clash and were favourites to make it five in a row, particularly with Leeds missing both Liam Cooper and Kalvin Phillips.
Despite good chances for both sides they went in goalless at the break, but the Whites played their trademark quick-paced football in the second half and Bamford scored three goals, two of them beautiful finishes, to put the Villains to the sword.
The performance and the result bore witness to how ingrained Bielsa's football is in his squad and how easily players can come into the side and perform as if they've played every game.
"We've been together for two and a half years now," said the head coach.
"The group is homogeneous and it's easy for everyone to assimilate their roles in the team."
One player taking on a different role was Luke Ayling, who replaced Cooper at centre-half, and Bielsa was fulsome in praise of the captain for the night.
"He was quick, he was agile, he defended well, he headed well, he used the ball well, he transmitted serenity to the rest of the team," said Bielsa, who made a vital 21st minute substitution that contributed mightily to the result.
Pascal Struijk, playing in Phillips' deep lying midfield role, took an early booking for a foul on Jack Grealish and could have seen red for a second challenge soon after.
Bielsa's concern led to the Dutchman's withdrawal and the entrance of Jamie Shackleton, who played superbly.
"Pascal picked up an early yellow and after this he had another foul which was a dangerous one," he said.
"There was a lot of mobility in the midfield, it was very dynamic and very easy for anyone to make a challenge out of time and I was worried so I made the substitution."
In a dynamic midfield, jet-heeled Shackleton is exactly the player you want. The youngster raced around the pitch, dribbling when he saw space and playing quick, clever passes when that was the better option.
He played a part in the move for the opener, too.
"He entered the game very well, he was dynamic, he didn't lose the ball, he won it back a few times and he had presence in the opponents' attacking third," said Bielsa.
But the headlines belonged to Bamford, who now has six goals in six Premier League games for Leeds, having struggled to find regular football and form in his previous top flight involvement.
"I'm very happy for him, he deserves it," said the Argentine.
"Everything that Bamford gets he deserves, not because I have any sympathy for him. From my point of view he's a player with a lot of qualities. He produces a lot more danger than he finishes and if he continues to improve his efficiency then he will receive greater plaudits.
"We haven't been doing anything different with him, he's been doing the same things he has been doing in the past. The only difference is he's now converting chances in the past he was not converting."
The hat-trick will add volume to noise surrounding the centre-forward's international future. He qualifies for both the Republic of Ireland and England but Bielsa refuses to be drawn on the subject.
One player who has a guaranteed future in an England shirt is Jack Grealish, but Leeds did a good jib of nullifying his threat, particularly in the second half.
He still created chances, seeing a first half shot cleared off the line by Ayling and a second half shot saved by Meslier, but he faded from the game as Leeds took full control.
"That was what we hoped for from the start," said Bielsa.
"Perhaps in the second half it was harder for him as when he received the ball he had less time to carry it than when he did in the first half, when he received it in more space. Nevertheless he's not an easy player to neutralise."