I haven't played her in so long, so the warm reception is heartwarming.
Bobbi will be glad to see Carol regardless, she can forgive and move on if everyone else can, and while she's not close to the mutants it'll be good to know there's a teacher around at least.
Clint's lack of utter disaster human will be strange to Bobbi at first, but she'll kind of respect it too. That whole still collecting women thing will not shock her at all. It's literally his thing. Apparently that and taking in strays right!? Fury is probably never surprised when Clint just appears with a new baby agent or former enemy!