Traditional tunes do not have an established, original version. No tunebook contains what would be called the definitive version of a tune. It is simply one arrangement of it. So, learning traditional tunes from written music is not the recommended way to do it. However, there's nothing wrong with doing it that way in my opinion. Here's one way of doing it.
Try to listen to multiple versions of the tune before playing it. Use You Tube, Rhapsody, your CD collection, archive.org, play along CDs, midi files, mp3's and so on. To this end you'll be familiarizing your ear with the tune. Then find as many different written sources for the tune as you can and compare them all. Some tips include searching online for the tune name + tablature, or + pdf, or + image, or + sheet music, or + notation, or + lead sheet. Many of these sites have audio to go along with the written music. It doesn't matter if the version you find was written for another instrument than what you play or if the versions you find are in different keys. You can learn something from all of them. Also consult all the tunebooks you happen to have for additional versions of the tune.
You can usually determine which key the tune is normally played in by the versions you find. If you find 4 versions and 3 of them are in D, then it's probably a D tune. See how it feels in that key. More often than not it'll be fine in that key. Or if you're feeling adventurous and want to explore a less familiar key, such as Bb or F, then try that and see how it does in that key. A basic understanding of scales and theory is required to do this, but it's quite simple once you grasp the concept. If the chosen key has notes or sections that provide difficulty, then sometimes a switch to another key can remedy that.
Mix n' match sections from all the different arrangements until you're left with a rendition of the tune that suits you. It's perfectly OK to throw in your own variations on the melody based on how you want it to sound. It's also fine to simplify or embellish the tune where needed in order to play it cleanly and the way you want. Once you have a rendition figured out, you can pretty much play it that way every time. Variations and improvisations will come naturally as you learn more and more tunes with similar enough licks. Or write out variations based on all the different versions you found. Once you play a tune long enough it will sound and feel like it was learned by ear. Eventually it will be committed to memory and you won't need the sheet music. But you can always fall back on it if you need to. Helpful or not?