#1
I figure out songs. That's the only way I practice. I find it makes my ear better.
So, should I write them out in tab? Will that make the song easier to remember or will it just make me to used to tabs?
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^thats a brilliant call. *jots in notebook*
#2
I find writing something down makes remembering it easier. It also means you can refer back to the tab, should you not feel like working the song out again.
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#3
I have a notebook somewhere of tabs I figured out. I kept them in case I'd like to look back over them.

Go for it if you have the time.
#4
Even better than tab would probably be writing them on the staff, as in actual musical notes. Bass clef. It'll make you more versatile as a musician--being able to read music and translate it onto the bass is an incredibly important skill (that I'm pretty much just starting to work on).