Music theory is really only a way of explaining sounds. In reality, you can sing any note over any chord as long as it sounds good. It is only when a note is held that it either harmonizes or clashes with the accompaniment.
The biggest step in learning to improvise is letting go and trusting your ear. You will obviously make mistakes as a beginning improviser, but the brain and the ear learn quickly and in time you will find more and more of the "right" notes naturally, just by practicing singing by ear.
Having said that, the more you know about how chords, scales and arpeggios relate to each other, the more options you will have when improvising. Any time a band is playing a Blues progression, you can use the Blues scale in that particular key. The previous example was in the key of Bb. Here is the Bb Blues scale. Learn the notes and then sing it from memory.