As far as I know, the only way you can change ability sets when playing online is to die at the hands of another player or get stunned in a "team" game. Unfortunately it's just not possible to commit suicide without getting assistance from your pursuer and it's inconvenient giving free points to a pursuer/target just because you want to change abilities.
Are there any other methods to be able to switch ability sets in the game that I'm not aware of?
On a side note, this question stems from this PC bug that prevents me from changing ability sets in team games between rounds. I don't get the "round changing" screen, I'm just left wandering the map until everyone else spawns which makes playing team games for me very frustrating.
Best Answer
There are unfortunately no other ways than the two you mention to change the ability set during a session. It's indeed sometimes frustrating as you say (even more I can imagine if you experience a bug on top of it).
If you have to die, try heading for an honorable death, canceling your pursuer's bonuses.