I rarely get involved in these sort of discussions anymore (where we ask for advice about beating one specific character), because I don’t particularly find them enjoyable anymore (because there’s a lot of debate that is going nowhere) and I find them complicated especially in PvP (Like in the OP’s situation, I didn’t really feel I could answer the question and there was only very little time to come up with one before the season was finished without getting more information). Like many others have posted, there are many answers and some might work for us, some might not. Some might like the answer, some might not.
For PvE where the levels of the opponents and who they are preset, it becomes easier to discuss and most of the time it also requires knowing more than just the team we use to successfully defeating a node, specifically their levels and which opponent to target first.
This is because for PvP there’s a lot of variables involved like what our roster is like (to know our MMR and what options we have), what level of the opposing character is (in this case Bishop), what kind of points we have for the event (to balance risk of retaliations and hits during hops), and also what the actual team is that we’re trying to beat (Bishop paired with Okoye takes a different tactic than Bishop paired with BRB or JJ).
Having said that, I can beat Bishop using my 4s. With my MMR, usually I have to rely on boosted 4s so I could deal with the other opponents. But, when there’s still a lot of time left in the event, I’ve used IM40 Peggy, IM40 Iceman, Vulture Gamora, etc. against 5*/Bishop teams. With my 5s, depending on Bishop’s level, I’ve had various results with multiple combinations of single 5, 5*/4* and double 5* teams. I know my 4*s are relatively high levels, but I’ve tried using my lower level duplicates too. I rarely hit Bishop teams on my hops, but sometimes if they are the only available points, then I’d risk it (sometimes by bringing my own Bishop).
Bishop is indeed another jack-of-all-trades character like 5* Gambit was, but because he’s a 4*, he becomes an option for 4* players to beat 5* teams. Not like Gambit where he was really hard to beat with 4* teams and even 5* teams. The 4* players hit the wall when Gambit was everywhere. At least with Bishop, there are many more ways to beat him. When the 5* players are unhappy, it’s usually because their previous hard work obtaining the 5*s became less of an achievement. I know not everyone has the time to play to get the characters at the same pace, so their experiences will be different and some of the players (if not most players) won’t have all the options to deal with him. The newer characters with an abundance of good blue powers also don’t help the situation because it makes it more appealing to keep using Bishop as an accelerator. WorthyCap is another option, but I have no patience waiting for the CDs to resolve and without Hawkeye, he’s not really reliable as an accelerator.
In this game, usually we could only say what is successful for us personally, unless we know from other people’s experience that a particular team has had a decent success rate against a certain character. The experience will be different to other players in a different situation and circumstances. It doesn’t mean any of the players are wrong or it’s a measure of the player’s skills or abilities if the suggested teams are not working.
Personally, I still think Bishop will be fine if we (or specifically the developers) manage to stop his AP generation and his passive becomes an active power, the exact moment the threshold is breached. At least that way there will be a predictable way of dealing with his passive. At the moment, if we are lucky to have a board that could make a lot of cascades, he could either make up to 30 blue APs or be downed without making any APs. If we’re unlucky, even when making a basic match-3 on our weak colours, we could get a big cascade that triggers his power multiple times. That’s not right.