Can we make a chart of any piece of music? Sure, pretty much. What about a classical piece? Absolutely. Here’s a bass exercise from one of my old lesson books, Wilhelm Sturm’s “110 Studies Opus 20, Volume 1”:

Figure 7.
Why would it be important to make a lead sheet of a classical piece? For performance purposes, there really isn’t (not by my admittedly limited experience anyway). But for practice, it helps to learn certain pieces. At points, the piece changes from F major to D minor and by condensing the notes into chords, one can see where the changes from major to minor take place. Other notation that may look confusing occurs, for example, in the last bar of the third line where one sees where I have marked it “Bb/D”. What that means is that the notes in that measure are actually an arpeggiated Bb major triad—Bb, D, G (remember the B is flatted from the key signature so no flat sign within the bar is necessary but the B is to be played as flatted). But notice the Bb is not the lowest note here but D is. So we notate that as “Bb/D” or “a B-flat major chord with a D in the root.” One will see this type of notation a great deal when reading charts.
Another reason the chord progression is important is for what are called head arrangements. Head arrangements are done without charts but are simply in one’s head. Many of the old jazz bands specialized in head arrangements or knew the charts so well they never bothered to look at them anymore. But doing a head arrangement on the fly is much easier if one knows the chord progression. Then it basically dictates itself.
In jazz bands, the custom is to assemble a book of arrangements in the form of charts and, in rare cases, the full sheet music. Many of these arrangements have been purchased and used over and over again by various bands, e.g. when Benny Goodman first started out with his own ensemble, he was using the arrangements of Fletcher Henderson. These are known as fake books—partly because they aren’t real books (I have a bass chart book that actually uses false titles for the songs to avoid copyright issues) and partly because a chart doesn’t depict a full score but just a skeleton and each musician will fake the rest. In the days when jazz was society’s music of choice, every band jealously guarded its fakebook so other bands couldn’t steal their arrangements.
Today, there is a very popular book of arrangements called “The Real Book,” the title being intentionally ironic, i.e. it’s a real fakebook. Every student of jazz has a copy. It has literally of hundreds of charts of every conceivable jazz standard. In fact, the “Satin Doll” chart in Figure 4 is from an edition of “The Real Book.”

Figure 8.
If one goes on websites dedicated to jazz, especially those geared specifically to musicians, one will encounter numerous threads dedicated to discussing the Real Book, many of them critical of it. Lots of musicians don’t like it because it’s too general and stripped down for their use. I sympathize, but, in many cases, there are few other references to look at and the charts in the Real Book, chintzy as they often are, at least offer a starting point. For example, the Figure 5 bass chart for “Satin Doll” offers no melodic line whereas the Real Book chart from Figure 4 does and this is what the musician would use to build a solo around. Now, I am simplifying here because “Satin Doll” is a pretty simple tune and the solo I play when I perform this piece is my own. I have never consulted anyone’s chart or recording for a solo. But more complex jazz pieces would require a melodic line written down as reference. The musician isn’t going to play it as written because it’s rather minimal but rather he is going to build off it and embellish it. I have also found the Real Book chord changes to be accurate and useful. If the chart is too simple then grab some manuscript paper and use that chart to build a more complex one. I have frequently made my own bass charts out of Real Book charts.
The jazz bassist needs to use the Real Book (and all the ones I know do) because it is always written in treble clef rather than bass clef and a good bassist must learn to read both. If you are a bassist and someone calls you up to perform in a paying gig, when you show, they are almost certainly not going to hand you a bass chart but rather a Real Book page or a copy of the pianist’s/guitarist’s chart or something like that. You should know how to convert treble clef into bass clef on the fly. That’s what my instructor did and he made me learn how to do it and it has proven itself time and again to be an invaluable tool.
If you are a bass guitarist, you can apply all these rules and pointers to your instrument. The only thing you can’t do is bow on your axe but jazz bass playing only uses the bow sparingly. In fact, I teach myself to play on the bass guitar everything I learn on double bass including classical pieces which I play pizzicato in lieu of the bow. If you are a bass guitarist, learn to play classical and jazz on your axe. Trust me, you’ll learn a lot about your instrument and yourself from doing it.