Is there any way to get from Bloomington (Indiana) to Indianapolis Airport for an early flight (pre-7am) by public transport?

My normal go-to for this sort of thing is Google Maps, but that doesn't have any public transport options shown for the route. I've tried Rome2Rio, which did suggest several good options for later in the day, but alas none that arrive in time

Hiring a car is certainly one option, as is taking the last Bloomington Airport Shuttle the night before and trying to find a cheap hotel at the airport.

Before committing to one of those options, I'm wondering - are there any other public transport options that might get you to the airport for a little before 6am?