Don't Bother Me was the first George Harrison composition to appear on a Beatles album wjen With The Beatles was released in 1963. This solo arrangement in the key of A Dorian (and occasionally A Minor) is how it appeared on my album A Beatles Collection in 1989.
I changed from the original key of E Dorian so the melody notes laid out better on the higher guitar strings, without getting too far up the neck or down on the middle strings.
The arrangement is not too difficult if you are already a bit familiar with keeping an alternating bass part going while picking out melody notes. There are a few barre chords involved, of course.