Do i have to download 6gb update on my ps4 to play offline ( no online mode) ps4

You dont need the update to play offline but you still need to be connected to the internet.

But i connected to my playstation shop, then i ran the game, it asked for an update .... just bought it so do i need to update it first ???

It says i need to update it to the lastest update in order to access the online features but i dont want to ☹️(

 You dont need to update it but the update has 2 new maps, new characters & they fixed the balancing of the characters. I would reccomend getting it as the game was a bit of a mess when it released the update fixed that.