Bale, 24, could make his bow for the Spanish giants at Villarreal this weekend, although his 32-minute cameo in Wales' midweek defeat to Serbia was his only football since mid-July.
Bale was greeted at Real by Cristiano Ronaldo - the man he replaced as most expensive player in the world - when he reported for his first day of training at his new club.
The Welshman will now have to cope with the attention that comes with being a 100million euro player, and the pressure of trying to justify his vast price tag.
Rush understands the challenges Bale will face, having spent a season with Serie A side Juventus between his two spells with Liverpool.
The former striker was signed for a British record fee by the Italian club, and knows an instant impact is required to win over supporters.
Rush, speaking as he hosted the FAW Community Awards presented by McDonald's at Cardiff City Stadium, told Press Association Sport: "A move like that is a massive adjustment and it is vital you make it as quickly as possible.
"He has not had any pre-season games and he needs that, the problem is when you become the world record player, the same thing happened with me at Juventus, it is the first impressions they will take.
"So I hope the media out there give him a bit of time as it might take him two or three games to get going, but sometimes in today's world it is about that instant impression and I hope he will be okay with that.
"He just needs games, sometimes he may be on the bench at Real, but the more he is on the bench the longer it will take him to get match fit.
"They have to start with him on Saturday, even if he only plays for an hour so, it gives you a chance to build him up. That's what they have to do."
But Rush believes Bale's work-rate will go down well with the Bernabeu faithful.
"When I pulled on the Juventus shirt for the first time I managed to score. It's a great feeling, the supporters want to be on your side," he said.
"I always gave 100 per cent and we know Gareth will give 100 per cent and that will get them onside.
"Everyone knows he has the skill but supporters really respond to players who give their everything for their club, it goes a long way."
The move to Real marks Bale out as one of the game's global superstars, but Rush believes he will also reap plenty of benefits on the field.
"He will certainly improve," said Rush.
"He is only 24 and now he will be getting that experience of European football so it will be a big education for him, as it was for me.
"When I came back from Italy I came back a better player, not a better goalscorer, but a better player. You learn about the game, the tactics and the technique at these top clubs and he will get better.
"He may not become the player people expect him to be, but he will be a better player.
"It may be that we haven't seen anything yet from him.
"A club like Real Madrid do not invest that sort of money if they don't believe you can get better. He will train with some of the best coaches and players in the world every day."
Bale was on official club duty on Thursday as Real unveiled their new third kit.
"It's an honor to be at Real Madrid and I've been made very welcome," he told realmadrid.com at the event.
"Everyone wants to win trophies with this club and the team wants to win all the titles it's competing for."