I have looked at the opening theme specifically to keep this brief and simple. The main melody that you have written follows a familiar pattern that can be defined in four stages: 1-2-7-1 (the numbers represent the values of the scale). As a composer, you should identify such patterns and formulate respective values that not only compliment but also counter that pattern. In my example, I have written 1-7-5-1 in the bass (it could also be written 1-7-2-1, depending on what you desire).
In addition to this, I have altered your cadence which marks the end of the pattern in such a way that makes it a little more interesting and refined. Also, at the end of a cadence, there opportunities for the lower parts to support transition to the new musical phrase, which I have done, again, in contrary motion to the upper part.
I then elected to modulate to B Major for it was convenient to do so from the 2nd degree of E Major (F#).
Finally, I also found 2/4 time much more fitting since you have effectively written two phrases of music that are each more clearly defined as 4 bar patterns.
Such designs originate from simple ideas. Robert Gjerdigen (a Music theorist who specializes in this kind of music) illustrates this rather well in the below video. The topic of the video is realization of partimenti, a form of exercise commonly used by students of composition during the 18th century. The student would identify standardized patterns written for either bass or treble clef and learn how to exploit them... much like how we have done here.