Not sure if this is widely known, but Cait likes when you walk around naked. If you fast travel naked between two different places, "Cait liked that" should pop up every other fast travel. Not too sure if the places matter, but I'm fast traveling between Sanctuary and Vault 111. Sanctuary being my current base settlement.
I'm still currently doing this, but I'm guessing you can max your relationship with her probably within an hour or two.