A good way to become more comfortable playing two parts is to practice the right hand by itself. This way, you can develop co-ordination between the thumb and fingers without having to think about the left hand at the same time. Here are some exercises to help develop your right hand co-ordination.
It is important to be equally comfortable leading with either finger when alternating. In this example, m plays the first string and then i follows. Once you can play it this way, reverse the order. This is a good habit to develop with all pieces and exercises.
As well as alternating i and m, it is essential to practice rest stroke with m and a. In more complex pieces you will need to use all three fingers interchangeably.
Once you have some confidence playing two parts with your right hand, try the following piece. In this one the treble and bass parts answer each other in a conversational style. This is called imitation, or call and response, which is a technique commonly used by composers.
Play it once beginning with i followed by m and then alternating throughout the piece. Then play it again and reverse the order of the fingers.
Once you are comfortable with this, use m and a until you are just as comfortable with them.
When you are counting, concentrate your count on the melody and the bass will flow along with it automatically. Be patient if you have trouble reading two parts at first. In time it will become second nature.