Warning: Mild Batwoman spoilers are ahead.
On the show, the Dark Knight's absence is the major reason Batwoman/Kate Kate (Ruby Rose) begins fighting crime in Gotham City. The premise is that Bruce Wayne/Batman disappeared three years before the start of the series. No one knows where he is, but the explanation for his absence is that he has "given up on Gotham City." Now the city is overrun with criminals, so Kate Kane takes to the streets as Batwoman to protect her town and the people she loves.
The comic book storyline is a bit more convoluted than that.
The show is taking its Batwoman storylines from both the 52 series that ran from 2006-2007 and from the Detective Comics series that ran from 2009-2010. In the 52 series, Batman, Superman, and Wonder Woman temporarily retire after the death of Superboy and Batwoman steps up to fight villains Bruno Mannheim and Black Adam. Batman reappears in the Final Crisis series in 2008 and is killed by another villain named Darkseid, but it is revealed in the subsequent Batman and Robin that Darkseid actually made a perfect Bruce Wayne clone to fake Batman's death and used his powers to send the real Batman to prehistoric times.
The 2010 series Batman: The Return of Bruce Wayne chronicles the Caped Crusader's journey through time to get back to the present day. Throughout all of this, Batwoman is fighting crime in Gotham. So perhaps the television show will eventually reveal that Batman is "dead," only to resurrect him after he battles his way through time.
However, Batwoman isn't at all about Batman, so the producers are in no rush to have the Dark Knight swoop back into town. At the 2019 San Diego Comic-Con, executive producer Caroline Dries said that while "anything is possible" regarding Batman appearing on the show, they also want fans to get to know Kate Kane on her own. There's also the issue of DC being fairly strict with the Batman intellectual property.
"As everyone in this room knows how strict DC is with letting us use the Batman property. They're just very careful with it because it's such a [big property]," says Dries, adding that they want to treat Batwoman a lot like how they treated fellow CW superhero show Supergirl.
"I think with Supergirl, as we were establishing her, we didn't actually want Superman right away. We wanted you guys to get to know her. I think part of Kate's journey is not to just fill these abandoned shoes, but to find her home. So, I think it's really important she has that time for all of us to spend with her and figure out what it means," said Dries.
Speaking to the 2019 TCA press tour audience in early August, Dries added that it's going to take time for Kate to even figure herself out as Batwoman, let alone have to worry about what happened to her cousin.
"[Kate] puts on that suit, as we see in the pilot, because she's trying to scare her enemy. She's not necessarily trying to become Batwoman," said Dries, per The Wrap. "She's just trying to disguise her identity and be a fearful opponent to her nemesis. So it's a gradual story. It's an origin story, so it's a gradual realization of, 'Oh, actually, I'm going to need my own identity.'"
So yeah, the Batman stuff can wait — even we even need it after getting to know Kate Kane.