The Serbian – who won three Premier League titles in his time at Chelsea – joined the Baggies on a free transfer last month after three successful seasons with Zenit Saint Petersburg.
Ivanovic has now impressed both on and off the ball in three outings for the club with the defender barking orders to help organise his team mates.
And Bilic believes the former Lokomotiv Moscow stopper is more than capable of playing in the Premier League every week.
“We go game by game but I don’t see why – if he stays clear of injury – that he (Ivanovic) can’t participate in every game,” the boss said.
“I see no problem there, he is not 42.
“He is 36 but people don’t question Thiago Silva, who is also 36 and has to play in the Champions League with Chelsea.
“He is also playing for Brazil, so you have to add another 15 games plus there is all the travelling.
“We don’t play in Europe and I think if you look at most clubs, they will have a player like Branislav.
“The way the players take care of themselves these days, the way they eat, their nutrition and their way of life – a player’s career has been extended a lot.
“He is a top professional, fit, naturally a strong guy. So I don’t see any problems with his fitness, especially when we are playing only once a week.”
Bilic continued: “Look at Pepe he is 37 and playing for Porto and Portugal. Luka Modric is 35 and playing for Real Madrid and Croatia.
“It’s not exceptional – it’s not like it’s Branislav Ivanovic and that’s it. Almost every club has a Branislav in their side.”
Bilic was also impressed with the way Ivanovic helped midfielder Filip Krovinovic during the 1-1 draw at Brighton on Monday.
With the Baggies chasing an equaliser late on, the head coach switched from a 4-3-3 formation to a 4-2-3-1 with Krovinovic playing in a midfield two for the first time.
“It was new (Krovinovic in that role),” Bilic said.
“We took some risks but he’s always there in my mind. He’s a player who is so comfortable on the ball – an honest player, with legs and everything.
“Filip is a top player. He also has to believe more in himself and risk more.
“He did exceptionally well against a Brighton team who is really good at finding those pockets.
“If he can do it against them, then there’s no reason why he can’t do it in the majority of the games.
“Barna (Ivanovic) was also really instrumental for Filip. I told him to lead Krovinovic, to where he had to be, left to right.”