I’m pretty sure Bluetooth is too slow for HDMI. I’m surprised the Chromebook won’t work with your iPhone. Once you turn on the iPhone’s personal hotspot, the Chromebook should see and treat it like any other wi-fi network. Note, it will not self discover, remotely turn on, and join the iPhone’s hotspot, like other Apple devices; but joining manually on the Chromebook after manually turning it on (on the phone) should work. Then again, I don’t own a Chromebook. Maybe Google did something odd with them. I say Google, because I have no problems with my Windows laptop joining my iOS hotspots. Heck, my Android tablets have no problem connecting with my iPhone’s hotspot.