“Bounce Man” is a transition from twenty one pilots' 2018 album, Trench, into their new era, as well as a continuation of the Dema folklore that was the centerpiece of their previous album.

Tyler stated that the song was about people drifting in and out of his life over time in the commentary below:

I try to keep, I like keeping the circle tight, I know that that sounds a little cliche, but it is very important to do. And as much as I like to do that, even looking back six years ago when I got married, looking at the wedding and who was invited there, it’s a different group of people than who I may have invited to that wedding if it were now though. So inevitably you’re going to see people coming in and out of your life and that’s very natural. It can be sad sometimes, but I do think that you start to realize that when those people start to cycle in and out, you start to truly recognize the people who are going to stay forever. When you realize who those people are, you get to lean into them even more. For me, it truly is family and it’s not always the case for everyone. Sometimes people have friends or long-time friendships that are just as powerful and strong as family. And I think that as I get older, I realize which ones are mainstays. And so, yeah, you’re going to have those people that come in and out but remember who’s got your back.

Within Dema lore, the song may be about Ned, a character who made his debut in the “Chlorine” music video and later appeared in the music video for “The Hype,” both seen on Trench. The first verse connects to a 2021 interview with BBC where Tyler was asked about Ned and said:

He turned his phone off. We can’t find him and he’s turned his location services off too.

In this upbeat, poppy song, Tyler tells Ned to leave and head towards Mexico where he will be safe, presumedly from the nine bishops of Dema. Interestingly enough, the Location Session for “Chlorine” included the coordinates for Mexico City, further connecting Ned to the song.