First it's helpful to define exactly what you mean by phrasing. For some, phrasing means the dynamic shapes, while for others its definition has more to do with rhythm. The best definition of phrasing I've heard was given by Kirkpatrick in his preface to a book of Scarlatti sonatas. He said that phrasing is the practice of grouping notes together. This involves seeing the piece as a series of "thoughts", or ideas, and you have to figure out which notes go with which ideas. As far as Bach's inventions go, you probably want to focus on communicating phrasing through the lengths of notes.
The way you do this is quite simple, in theory. For notes that are part of the same idea, or phrase, you will play them more legato. Between phrases, you will not be legato - you want to put a bit of space, or daylight, between successive thoughts. Space between thoughts leads to clarity.
Of course, it is very easy to go overboard, as you have experienced. When playing Bach, for example, phrasing is in the "too much" zone if the basic tempo and pulse of the piece cannot be detected. (I am sure there are exceptions, but I think this is a safe thing to say for the first Invention.) It is also too much if the ending note of every phrase is cut to a ridiculously short staccato and everything else is a watery legato.
In the end, it is a question of knowing what is enough. There are a few ways that I know of to cultivate this subtle perception.
1. Listen to lots of recordings of the piece and listen several times for only the phrasing. See how different performers group notes together and listen to how obvious or subtle they make it.
2. Learn to sing. Or at the very least, imagine the melodic lines being sung. Often, the perfect phrasing, especially for baroque and classical music, is achieved if you imagine that an opera singer is singing the line. Where he or she would take a breath tends to be the perfect place to end the phrase, and the length of that imagined breath will help you with the amount of space you want to put between phrases. If you have ever played a wind instrument, you also have an advantage, because the way you breathe in playing a wind instrument can also be greatly beneficial in teaching piano phrasing.
3. Learn the following terms and concepts. Discuss them with your teacher, especially on how they relate to good phrasing:
cadence
modulation
melodic curve
phrase vs. period
elision
Let me know if anything needs clarification, or if you'd like to discuss any of this further. It's a good topic!
Topic: Phrasing in Invention no.1