Kill a bug:
Roadhog
Junkrat (if they're bothering him)
Soldier 76
Sombra
Torbjorn
D.Va
McCree (if it's something like a spider or a fly or something; if it's a moth or ladybug or something he'll move them outside if he's near a door or window)
Zarya (if they're annoying her)
Ana Amari
Moira
Takes the bug outside:
Zenyatta
Lucio
Genji Shimada (unless it's hiding from the cold or something)
Mei (she'd let it stay but Snowball will try to play with it which might not end well for the bug anyway)
Bastion
Orisa
Also D.Va (if she's near a door or something)
Hanzo Shimada
Winston
Brigitte
Mercy
Symmetra
Pharah (she'll usher them with a foot or a paper or something; not a fan of touching bugs)
Tracer
Leaves the bug alone:
Also Junkrat
Akande (as long as it's not in the kitchen or his room or something; if it is he'll move it outside or elsewhere)
Also D.Va (if she's too busy to bother with it)
Also Winston
Reaper (unless it's near food, then he'll move it)
Also Brigitte (she likes to make small talk with the bugs if they're hanging out while she's doing something)
Also Symmetra
Reinhardt (he also likes to make friends with them)