Head coach Zidane claimed in July it would be better for all concerned if Wales star Bale were to leave the club, but a move to Jiangsu Suning in the Chinese Super League collapsed.
With no other options for an exit materialising, Bale was a surprise starter in the LaLiga opener against Celta and responded with an excellent display, setting up Karim Benzema for the opening goal of the 3-1 victory.
Madrid boss Zidane confirmed after the game that Bale would be staying at the club, and he now wants the former Tottenham man to perform consistently to the standard he hit at Balaidos.
"It was a good game by Gareth," Zidane said on Friday ahead of Madrid's meeting with Real Valladolid. "He worked hard defensively. We want to continue playing this way.
"We need to improve to achieve good things this season. These are talented footballers who want to play, and I want all my players to play a part.
"What we want from the players is that they want to remain at the club, want to be here. A lot of things were said but now he wants to stay, we want him to play a part. He' s an important player, he's proven that in the past and he has to do that again, to show just how good he is."
Zidane has similarly challenged James Rodriguez to impress, the Colombia playmaker another to find himself surprisingly back in the Madrid first-team picture as prospective moves to Atletico Madrid and Napoli have failed to materialise.
"We're happy to have James back here at the club," Zidane said. "Let's see how things progress going forward. He's happy to be here. There are lots of games coming up and all the players are going to have a role to play."
When asked if James could replace the suspended Luka Modric against Valladolid, Zidane replied: "We'll see. We choose 11 and three players could come in. And we have 24."