I don’t want to make you feel bad, but because so many writers handle this issue badly, I’m going to discuss the use of bad and badly.
Let’s start with badly, which is an adverb. Roughly speaking, an adverb describes how something is done: “She handled the news badly.” Bad, on the other hand, is most familiar to us as an adjective, but what stymies us sometimes is that it can also be an adverb.
In adjectival form, bad provides detail about the noun it accompanies: “I have a bad feeling about this.” As an adverb, bad modifies the preceding verb: “Now I don’t feel so bad about it.”
If you’re in doubt about which adverbial form to use, test it by replacing badly (or is it bad?) with a synonym, such as poorly. (“She handled the news poorly.”) That looks and sounds right. But would poor work? (“She handled the news poor.”) Definitely not; the form badly is correct.
Now test the sentence that uses the adverbial form of bad: “Now I don’t feel too poorly about it,” or “Now I don’t feel too poor about it”? Hmm — I’m not sure. So I’ll try another synonym: “Now I don’t feel too wretchedly about it,” or “Now I don’t feel too wretched about it”? The short form is the clear winner here.
But why? What’s different about the two adverbial forms? The issue is complicated by the fact that two types of verbs exist: action verbs and linking verbs. Handled, in the first example above, is an action verb because she handled — she did something. Linking verbs, on the other hand, describe a state of being: I think, therefore I am.
One set of verbs that can perform both functions — action and linking — are the sense verbs, including feel. (The others are look, smell, and taste; I’ll discuss the omission of hear later.)
The sentence “I feel the breeze” refers to an action; your body is responding to the breeze. If you are unable to feel the breeze because your skin is not sensitive, you could say, “I feel the breeze badly,” in the sense that your body is ineffective at feeling the breeze. (This usage is awkward and therefore rare, but it is correct.)
However, if you’re using feel in the linking, or state-of-being, sense, feel refers to your emotions, not your tactile ability. If you have asked someone to join you on a walk, and the person is bothered by a strong breeze that suddenly whips up, causing some distress — oops, there goes the hat! — you could say, “I feel bad about the breeze.”
Wouldn’t badly work just as well? Apply the synonym test: “I feel wretchedly about the breeze.” Clunk. “I feel wretched about the breeze.” Click.
That explains why you want something bad, not badly. (To want something badly is to do a poor job of wanting it — almost the opposite meaning.) That’s why you’re not doing too bad, rather than badly, right now. Bad is a condition (a linking verb), not a performance (an action verb).
So, why isn’t hear an action verb, like its sensory siblings? You can write, “That feels disgusting” and substitute feels with looks, smells, and tastes, but “That hears disgusting” doesn’t make sense; we replace hears with sounds in such constructions.” Why is this so? I can only give you my stock answer for such curiosities: It’s English.