When people use "a bit too" + positive adjective, they actually mean the opposite.
"She's a bit too nice" = "She's not really nice but she pretends to be nice"
When you use it with a negative, would you mean the opposite?
"He's a bit too stupid" -- would this mean that he's really smart? It could, but usually it doesn't. When people say something like that they just mean that he's really stupid. Just scanning the first few pages of the Google results you mentioned, it's obvious that people are using this construction with the negative adjectives simply as an intensifier. This is not how this construction works with a positive adjective.
Your example with "ironic" similarly doesn't really work to mean the opposite. "He's a bit too ironic" -- does this mean he's not ironic at all? That would be absurd. To be too ironic, he has to be ironic. What this would mean then is simply that he's really ironic; he's being ironic too much.
While with a positive adjective this can be sarcastic, it's not sarcastic at all with a negative one.