The correct spelling of the phrase "am bottom of" is determined by the phonetics of the words involved. The sound "am" is pronounced as /æm/ in IPA transcription, while "bottom" is pronounced as /ˈbɑtəm/. Thus, the correct spelling is "I'm at the bottom of", with "I'm" being the contraction of "I am". Understanding the phonetic transcription of words can help improve spelling accuracy and pronunciation clarity.