Over the years since Arrow premiered back in 2012, the Arrow-verse has grown to include a whole bunch of superheroes of DC Comics legend, but the Dark Knight of Gotham City hasn't turned up. For a long time, the only Arrow-verse show to actively tease Batman was Supergirl, which is set over on Earth-38 and has the freedom to refer to Batman without introducing him into the world of Oliver Queen and Barry Allen and the Legends. The past year has given viewers reason to wonder if he really could pop up, however, to the point that The CW president Mark Pedowitz weighed in on the possibility of Batman in the Arrow-verse, saying this:
There's no discussion about a series. Batman already exists in the Arrowverse because last season Oliver Queen mentioned his name at one point. And Batwoman, if the series goes forward, lives in Gotham. There's no plan at this time to have Batman appear.
Well, Batman may not be gearing up to drop by Star City or Central City any time soon, but he evidently exists in the Arrow-verse, and Mark Pedowitz's reference (via EW) to Oliver's mention of Bruce Wayne seems to indicate that Batman exists on Earth-1. Bruce Wayne and Gotham City actually got their very first explicit Arrow-verse mentions last fall in Arrow's sixth season when Oliver tried to deflect accusations of vigilantism by claiming that Bruce Wayne could be the Green Arrow. If Oliver has secretly known that Bruce Wayne is Batman all along, that little comment probably didn't endear the Emerald Archer to the Caped Crusader. At the time, the Bruce Wayne mention could have just meant Bruce Wayne, no bats involved.
The case for Batman in the Arrow-verse got stronger this summer when news broke that the big crossover in the 2018-2019 season is going to feature Kate Kane, a.k.a. Batwoman, based out of Gotham City. If one Bat-themed vigilante is based out of Gotham in the Arrow-verse, why not two? At the moment, The CW clearly only plans to introduce Batwoman.
As far as I'm concerned, Batwoman is enough for now. Her introduction in the crossover will mark the first time Kate Kane is adapted into live action. If her series gets an order, she would be the center of a superhero project unlike any other on the small screen. If the Arrow-verse introduced Batman in the next season, he could overshadow Batwoman, just as Superman would have likely overshadowed Supergirl if he'd turned up right away on Supergirl.
Besides, if anybody needs a Bat-fix, they can always check out Gotham. Young Bruce may not be Batman yet on the Fox series, but all the Bat pieces are in place. Arrow-verse viewers can enjoy Batwoman in the crossover and perhaps her own series. We already have our own theory about how she should be introduced into the Arrow-verse, and the only downside is that we have to wait until fall to get a look at her in action. For now without Batman, we can make do with mentions of Bruce Wayne or Supergirl jokes about Superman's grouchy friend with all the gadgets.