It's in E, but I had to tune the recording up 60 cents. The low open E string gives it away. I've never learned tab, but maybe someone else can help out. The first bass note is an F. Then it's mostly the E on the A string, the G on the D string, and the A, B, and open E on the E string. The fourth measure of the bass line has a little fill that starts on the D of the G string, then D#, E, then A, A#, and B on the D string. I hope this gets you started.
In terms of advice, I echo most of the advice you'll get on this forum. If a teacher is available to you, take advantage of that. Even a handful of lessons will help avoid bad habits. There's a great thread here on TalkBass on getting started. If a teacher isn't available, start learning theory so that the notes make sense. Some people swear by YouTube videos.
If you really want to learn songs by ear, specialized software helps. You'll see lots of opinions that too. The choices include ASD (Amazing Slow Downer), Transcribe!, and Audacity. The software allows you to tune the recording to your bass (as I had to do with Here's To You), loop sections, slow it down, adjust EQ, etc. You'll have to use MP3 files instead of YouTube links.
You'll get all kinds of advice on developing your ear. I find that methodically learning songs (with the help of software) is one of the best ways to recognize intervals and rhythmic patterns. Learning theory helps you understand what you're hearing.
Best of luck to you!