In Bounty Hunter mode, whoever becomes the Target receives an instant Ult charge so you won't have to wait long to find an opponent who is ulting. Also, remember that the Target is highlighted through walls so you can easily find your way towards them. There is a big part of luck and opportunism involved so just keep playing and pay attention to any Ult line. One thing that might help is that Targets will sometimes bet on their Ult to unlock
so players who haven't unlocked it can sometimes be desperate and Ult any chance they have so stay on the lookout.
From my own experience, this mode is played by a lot of Pharah, Reaper, Widowmaker, Soldier 76, Junkrat, Genji, Bastion and Doomfist.
I'd suggest dropping everything else and try to flank the Target if you hear an Ult line coming from : -Pharah (stationary and locked towards one direction, easy to get behind)
-Reaper (slowed down by their Ult, good if you can attack them from afar without getting too close)
-Soldier 76 (lasts for a while, you can try and let other players weaken them before moving in for the kill)
-Widowmaker (also lasts a while, might lead to the Target focusing on their headshots for "Quick on the Draw" so you can flank them but even if they spot you, Widow can be easily outgunned).
Be wary of :
-Junkrat (usually ults to become the Target, not once they're it / on the other hand, if you are Junkrat, keeping your Rip-tire under your hat and waiting for a Target Ult can be a good play !)
-Genji (quick and hard-hitting in close quarters, you might not want to challenge them mid-Ult depending on your character)
-Bastion (as devastating as Genji if it nails a direct hit but slower, so you can try a flank)
-Doomfist (run for your life if they Ult, impossible to intercept).
TLDR : be observant, opportunistic and agressive when needed, know when to challenge and when to wait for a
weaker better prey.
I'll update this list with your suggestions if you have other "good targets" or strats in mind. Feel free to dislike but please explain why and remember that everyone's personal experience will differ so what worked for me might not for you and vice versa. In the meantime, good luck and may you have a bountiful
pun intended match.