Congratulations on playing by ear ... it's a great way to start out, IMO.
You don't seem intimidated about notation, and that is great ... it may be most of the battle. Musical notation is just a kind of code that's not so hard to read and write, if you know how ...
I think you should start by learning to read the notes from your fingerboard as you play. There are 12 kinds of notes. You could get started on your favorite tune by just making a list of the notes as you play them.
Here is something you could use to read the notes off your fingerboard: http://www.instrumentalsavings.....0chart.jpg
After you make that list you will know what notes are in the tune. Very often there are exactly seven kinds, and those seven determine the key signature, very simply. If there are other than seven, it will be a little more complicated.
You will also have to choose a time signature and find patterns in the rhythm.
When you are ready to write the actual sheet music, you can use the Musescore program. It is free from musescore.org, and there are good video tutorials on how to use it.
But yes, I would say to start writing the letter names of the notes that you read from your fingerboard. But my advice is to not stop there or get sidetracked into tablature.