Bale will be the centre of attention at the Cardiff City Stadium as Wales host Iceland in an international friendly on Wednesday night.
The former Tottenham star has started to hit form at the Bernabeu after a slow start following his £85.3million move last summer due to niggly injuries.
Bale has scored five goals in his last seven games for a Real side who are top of La Liga, through to the Copa del Rey final and on course for the Champions League quarter-finals.
The 24-year-old has become one of the most recognisable players in the world but Williams claims the fame and potential glory has not changed him.
The Swansea defender said: "There's no difference, he's the same guy.
"I don't think he will ever change. He is a nice, genuine lad.
"He's here the same as everybody else, the same as before.
"Nobody is treating him differently and he's not acting any differently."
The only changes Williams expects might be in his performances - which were already of very high standard - having fed off the likes of Cristiano Ronaldo, Xabi Alonso and Luka Modric.
Williams said: "Playing with those type of players at Madrid it is probably only natural he has got better - if that is possible.
"So I am looking forward to playing with him again."
Real's demanding schedule has led to suggestions that Wales might be under pressure from the Spanish giants to use Bale sparingly.
But with the visit of Iceland one of only two friendlies before the start of Euro 2016 qualifying, manager Chris Coleman is prepared to maximise the availability of the Cardiff-born player.
Coleman said: "If he starts we are looking to play him for 90 minutes.
"We want to win the game. We will have to go into it with the right mentality and start with our strongest team."
Coleman believes Wales have a strong chance of qualifying for an expanded European Championships having been pitched into a group with Bosnia, Belgium, Israel, Cyprus and Andorra.
For that, however, he knows his top players must play together as often as possible.
Coleman, who signed a new contract last November, said: "We have got good enough players and if we get them together enough I believe we will be successful in this campaign."
Iceland, who reached the play-off stage in World Cup qualifying, might provide a good yardstick.
Coleman said: "It just shows you what can be done if you field your strongest team more often and I think they were able to do that."
Williams is fit to play after illness - he was sick on the field - curtailed his involvement in Swansea's draw against Crystal Palace last weekend. Palace midfielder Joe Ledley has withdrawn after suffering a hip injury in the same game.
Arsenal's Aaron Ramsey was already unavailable.