The 1st 4 notes(+ the 2nd group of 4 notes) looks like an E Major chord(B-E-G#).
...have you tried playing an OPEN "E"?
I'm assuming you tried playing "B" because that's the guitar's 1st note(?).
Think of it like a pianist...the guitar part is the Right Hand, your Bass note is the Left Hand.
The next group of notes could be an E Major w/ an "A" as the bass note(A-E-G#).
Since you mentioned a this as a "Punk" tune-
In addition to hammering out the Roots...think/try to add(maybe) the 3rd or 5th.
Try something like this(all 1/8th notes for you...if this sounds 'busy', try something else)

lEE EE EE EElG#G# G#G# G#G# G#G#lAA AA AA AAlBB BB BB BBl
Or-
lEE BE EE BElEE BE EE G#G#lAA C#C# BB C#C#lAA BB GG F#F#l etc