I Strongly Encourage you to Wait before Investing in Bullseye
So there’s already already a thread speculating his nerf during the rebalance period up, but the thread seems to be going off topic. Due to that and certain comments confirming what I was already beginning to theorize, I felt I should make this thread in advance to warn players not to go all in and balls to the wall on ascending or r5ing him yet.
To keep it short, even if he survives the rebalance period (we have yet to see any champion nerfed during one so far), the probability of them releasing champs to completely shut him down are high, especially when you consider the feedback they got from all the people that complained about him during the very first month of his release.
Remember Peni? Just like Bullseye, she had that unavoidable damage in her kit and she was the go to defender back during her release. However, after Galan and Hulkling were released , people just completely stopped using her for defense in BGs
One other thing to keep in mind is that even if certain champs that are bleed immune work for him in BGs, that if they ever designed him as a boss for challenging content in the future, that said champs may not work there and more ideal counters may be required, thereby opening the gates for them to release hard counters.
Now ofcourse you can make the argument that ascension dust is becoming drastically more available than it once was and that you can just use the magika gem to r5 him, but in case you cant get the gem anymore or want to use it on someone else, this notion could be worth considering.