I've both played and written a lot of advanced solo string music, and, while it varies from composer to composer (and editor to editor), bow markings are not at all uncommon. I just grabbed two scores off my music stand—Britten's Three Suites for Cello and Hindemith's Sonate for solo cello—and the former is covered with markings while the latter has none at all. As a player, there are some bow markings in the Britten that I think are completely unnecessary, and there are parts of the Hindemith where I wish he had given a bit more guidance (he was a phenomenal string player after all). To some extent, you're touching on one of the oldest debates in composition, engraving and general notation theory: how much is too much? Too many markings make it more likely that players will be overwhelmed by your overnotation and start to miss or ignore it; too few markings can leave your intention unclear and make the player have to do too much work figuring out the best way to realize your musical goal. I should note at the outset that, as a composer and a player, I tend to land further toward the overnotation side than the undernotation side. Still, I think there are several different reasons to consider adding bow markings to an advanced score, and I'll try to give examples of some of the most important.
- "Feel" vs. Reality
The very first measure of the first cello suite by Britten has this notation:
I would argue that the initial downbow is pretty pointless, but the down followed by an up on the fourth beat is definitely important information. The tied Bs indicate that this should be done in a single bow, but playing the passage that way would have ended up either requiring beginning or ending the passage awkwardly with an upbow. As written, without the bow indications, there would be four strokes in this passage, and this means a compromise has to happen somewhere. Britten or his editor chose to leave his original notation in place, but add bowing indications from Rostropovich, the cellist that premiered the piece. Personally, I don't love this kind of conflict between two different kinds of bowing indications, but it works and is clear enough.
- Unusual bowing situations
Here's the second measure of the fourth movement of Britten's first suite:
Here we have a pretty unusual use of the bow. It is uncommon to use col legno in this manner, and the bowings are pretty helpful, or at least I found them to be. They definitely run counter to what I would have initially tried for the passage, but it ends up working surprisingly well.
- Bowings contrary to defaults
If you've written a pretty basic 4/4 part with an obvious pickup note into a strong downbeat, then it would be fairly silly to add an upbow marking to the pickup note and/or a downbow on the downbeat. That's very standard bowing practice, and you're just wasting ink unless you're writing for amateurs. However, if you want the pickup note to be played down and the downbeat to be played with an upbow, then you had better give us an indication. Here's a moment from the beginning of the last movement of the first suite:
Again, this is the very first measure of the movement, and it is not at all likely that a cellist's first instinct would be to play this passage starting with an upbow. There are several possible reasons that Britten (or Rostropovich) chose this bowing however. For one, this movement is supposed to sound like it has suddenly come out of the previous movement. Another is that it lends a slightly unusual accentuation to the pattern, which continues in the rest of the movement. It also puts the player in mind of just how delicate the start of this movement should be (because it is wall-to-wall sixteenth notes and could easily inspire the player to play it more heavily than it's supposed to be). Not everyone would agree with the choice, but even if they personally decided to start with a downbow, the indication would still make them give it a greater lightness than they might otherwise have used.
- "Special effect" bowings
The most common bowing effect that more or less requires markings are situations where a double down or double up bow are called for. To be sure, these kinds of bowing are sometimes added by players on their own, but if you want a super-pesante, heavy style, it isn't unreasonable to ask the player to use multiple downbows in a row. Here's an example from the second movement of Britten's second suite:
This is not at all the first, second or even third way I would consider bowing the passage, but now that I've tried it out, it's a very nice effect. It gives the line a heaviness that will make more sense later in the movement, and it helps emphasize the almost-halting quality of the rhythm.
The bottom line is that there can be great reasons for bowing markings beyond coordination of a section or amateur instruction. No two composers or players will agree 100% on how much is too much, so, to some extent, you just have to look at scores of pieces you admire in a wide variety of styles until you start to develop your own sense of what's useful and what isn't. Have fun with it!