Is there a reason you don't want to just bike? Seems like the perfect distance for it, and it's free after the initial investment of a couple hundred dollars.
Depending on that 3 mile commute (hills, traffic, bike routes), it may also be faster.
Also, before they put the bike lanes in biking during rush hour felt stressful and dangerous.
That said, a lot of people seem to sweat less on bikes with an electric assist; people worried about sweat might look into those as an alternative.
And learning to ride it :)