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how long is it and what format/codec did you edit in?
you could start by exporting at 720p with a bitrate cap around 8000kbps. The quality should still be reasonable, and it is similar to what many people upload to youtube/vimeo. if this doesn't get it down to the right size, it will at least give you an idea of how far you need to go. Also, why 120mb? vimeo is 500mb for non plus/pro members, and i think youtube is unlimited (the only reason I use youtube is because I do not have a plus account, and I had some videos that were well over 500mb after i exported)