The first question you need to ask yourself is "what chord fingerings will I be using when play this song?" Country blues songs tend to use a lot of open major and 7th chords -- C's, G's, D's, A's, E's (although the old masters obviously throw in a lot of exceptions). These happen to be some of the easiest chords to play, so you're in luck.
Before you start learning an alternating bass song, familiarize yourself with the chord progression and fingerings you'll be using. Let's start with our example. The example follows an 8-bar progression that uses these fingerings, with each chord played for 1 measure except in the 7th bar:
Always familiarize yourself with the fingerings before learning the bass line and melody -- if you try to learn the bass line or melody using the wrong fingerings, you will develop bad habits that are hard to break. Also, if you are thoroughly acquainted with the fingerings and able to move between them fluidly, then you will have a much easier time picking up the melody and bass line and putting the whole song together in a way that flows. That being said, try playing through the example below using the chords and getting used to making the changes fluidly. The drums are added here to help youn keep time, if you don't like them you can turn them off by unchecking the box marked "Groove".