Record transfer signing Rodrigo started against Manchester United last Saturday but was withdrawn at half-time with Leeds struggling to contain the Red Devils' midfield and he was only named among the substitutes for today's 2-2 draw with the Toffees.
Bielsa opted to keep the Spanish international on the sidelines, sending on Tyler Roberts to play the number 10 role in the second half when replacing Mateusz Klich.
The head coach would have played Rodrigo from the start, however, had he not picked up a niggle in training.
"During the week he had a slight muscular issue, from which he recovered quickly," said Bielsa.
"If that hadn't happened he would have been our offensive midfielder in the game today."
Last season was a frustrating one for Rodrigo after a £27m move from Valencia, injuries and Covid-19 disrupting his rhythm and preventing him from showing the best of his ability. He did end the campaign on a high however with a flurry of goals and impressed Bielsa with his efforts both during the summer break and once pre-season began.
The head coach hopes Leeds fans will get to see the best of the attacker this season.
"I have a lot of confidence in the qualities of Rodrigo," he said.
"During his holidays he did physical work that was very important. During the six weeks of pre-season he's the player who shone the most in those weeks. I have a lot of hopes for him that in this season he is going to show all the qualities he has. In the game today I opted to put Klich and Tyler. He could have played, that's why he was a substitute but I preferred that the two players that I named came on instead."