You actually ask if the auxiliary verb (am) refers to the word "busy" or to the word "learning". I think that you asked this question because you assume that if it refers to the word "busy" then the word "learning" is a gerund, and if it refers to the word "learning" then the word learning is a verb in present participle tense.
I guess that it's not simple to answer on it since not any case in English has rule, but personally I believe it depends on the context and meaning of the phrase. That says, that if you say your phrase in following meaning:
I am busy learning English. = I am busy in nowadays because I have a lot of learning.
then in this meaning the word "learning" is gerund, since it functions the same as if was written: "I'm busy in learning English".
But if you say your phrase in this meaning:
I am busy learning English. = I am busy right now because I'm learning English.
Then, it's as if was written "I'm busy now because I'm learning English" since there is a using of pronoun + auxiliary verb in this sentence (I am...), near to the word which ends with -ing ending, therefore it is a verb that functions as present participle.
It cannot be a gerund, since the definition of gerund is "form of a verb which acts as a noun". In your case it does not acts as a noun because of the presence of the pronoun (I) with the auxiliary verb (am) right before the word ends with -ing.
If you wrote "Learning English makes me busy", or "Learning English is easy" then the word "learning" would be a gerund in both of these sentences because they are themselves the 'instead of' the pronoun, the subject of the sentence rather than additional to it.
BTW, I found similar question in this forum and you can see another opinions.