Bale has not always been a regular in the Madrid XI this season and his appearances were loudly jeered in the final weeks of Santiago Solari's unsuccessful tenure as the team's challenge faded in three competitions.
The Wales international was restored to the starting line-up and scored in Zinedine Zidane's first match back at the helm, but his future in Spain remains far from certain.
Bale openly discussed his desire to leave Madrid under the three-time Champions League-winning coach at the end of last season.
The former Tottenham winger must still win the fans back, too, and Van der Vaart, who played for both Madrid and Spurs, is unconvinced that Bale is cut out for the battle.
"Gareth is an amazing player but he's a person that has to feel the confidence," Van der Vaart said. "He has to feel he is welcome.
"But I know Real is a difficult club if you don't perform. It doesn't matter if you're [Cristiano] Ronaldo, Bale or Van der Vaart – they'll throw you out after just one year.
"You have to deal with it – and I don't know if he can do that.
"I know him as a person and, with a Spurs hat, I always hope he'll say, 'OK, I'll come back'. I don't think it's going to happen, but that would be a nice story."
Musing over how Bale might turn the situation around, Van der Vaart suggested the 29 year-old needs to be more selfish.
"It's strange but, in Holland, we say that sometimes you need to be an a***hole," he said. "You can also be a positive a***hole.
"He's worth €100m – they paid a lot of money and he has to do it. In his last year at Spurs, he took every free-kick, he decided everything.
"That's what he has to do now. I realise it's difficult, because you have so many good players, but he should do it more."