and bebop in general definitely does resolve. The genius of Bird's solos is in the way that they resolve. In pop music, we tend to look for cadences at the end of a chorus, maybe a tag ending or the ninth bar of a blues. In other words, tension is built up and resolved over a longer span of bars. In a bop solo, tensions can happen in the melodic structure and be resolved in a matter of a few notes.

Here's an example of a typical bop resolution: play the flat 5th interval of a chord, skip forward to the 6th and then step backwards to the perfect 5th. Here, the dissonance comes courtesy of the flat 5th which is then resolved by ending the phrase on the more consonant perfect 5th.

It's the constant cycle of introducing non-chord tones in a melody and then resolving them on chord tones that makes up a lot of what you hear in a bop solo.

I hope this helps some.