Watch the The Architecture of Bebop online guitar lesson by Fareed Haque from Bebop Improv Survival Guide
There are many benefits to learning to improvise thru the arpeggio approach.
First off, it's historical. You will be learning the same way the jazz 'greats' did. Arpeggios allow you to put together chords and scales based on what your ear tells you…so you will naturally explore, by ear, different musical possibilities that appeal to you. As such you will naturally create your own choices and embark on the path to your own unique and individual style.
Monk chose different notes than Bird did...and so will you! As a guitarist, this approach is also empowering. Make sure you create an arpeggio fingering to go along with every chord grip you know. As you learn more chord grips, you learn more chord arpeggios. Once you have a chord arpeggio you like, fill in the notes in between BY EAR.
An arpeggio is ussually 4 notes 1,3,5,7 ...thats already 4 notes out of the usual 7 note scale! So all you need is to add in BY EAR the remaining 3. You will find different possibilities. They are ALL Correct.
Some will be harsh ["dissonant"], some more sweet ["consonant"], some downright UGLY! Explore! The next step is to start leading to notes in each chord chromatically from above or below.
Once you have many grips and lines you'll start to find that you can add chords thru arpeggios to any progression. C Maj7 goes to Dmin7 to G7 and back to C Maj7. This is a typical I-ii-V-I jazz prgression. We can add chords to this progression. A common example is adding a Dominant chord to lead to another chord. Typical in this case might be to add an A7 to lead to D min and then add a D7 to lead to G7. These chords will clash a bit with the basic chords. That is the desired effect! You are playing 'outside' the chords and leading back 'inside'. That's what makes it cool.