With the exception of the Eternal Mangekyou Sharingan and the Rinnegan, the Sharingan doesn't seem to flow well with the human body. The Mangekyou causes its user blindness, and the Sharingan is prone to causing the eyes to bleed if overworked and overstressed.
Sasuke's and Itachi's eyes bleed when they summon their Amaterasu black flames, showing how much stress and strain using Amaterasu and Flame Control puts on the eyes. Amaterasu in particular seems to have an extra nasty side effects in comparison to other Mangekyou abilities like Kamui, which never cause the Sharingan to bleed. Judging from Itachi's and Sasuke's reaction to when they use Amaterasu (especially for the first time), the jutsu evidently causes its caster a lot of pain.
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Susano'o seems like it might inflict the most pain of any Mangekyou Sharingan power, since Sasuke described using Susano'o as feeling like "every cell in his body was on fire", evidently meaning that summoning a Susano'o requires a lot of effort and takes a heavy toll on the body.
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Sasuke's not usually one to complain about pain, but the fact that he even voices how painful using Susano'o is speaks to just how excruciatingly painful summoning and sustaining the Uchiha's avatar must be for its user, since Sasuke didn't even mention the pain that the Amaterasu caused despite it making his eyes bleed. But it appears that using the Susano'o is even more painful still. So presumably, every time an Uchiha summons the Susano'o, it is very painful for them to do so. Evidently, the Uchiha clan members are insanely pain tolerant.
The Eternal Mangekyou Sharingan might work better with the human body and therefore might make it much less painful to use Susano'o, but that is merely my personal speculation.
Alternatively, there's the possibility that it takes a while for the Mangekyou Sharingan to settle in one's eyes, and Sasuke's pain was caused by him using his abilities too much and too soon (which he definitely did). In this case, perhaps Susano'o only causes a lot of pain to those who overuse it too soon after their Mangekyou awakening. Then again, Sasuke hadn't used Susano'o all that much at the point where he described the excruciating pain of it, so mostly I'm just going to assume that all the Uchiha are we see using Susano'o are pushing through the pain.
Sarada's Phase I Sharingan also bled when she was training, showing us that any level of Sharingan can suffer from being overworked or over-strained. I suspect hers bled more easily because her one-tomoe Sharingan was too weak to keep up with the pressure of tracking so many projectiles and her eyes lacked endurance. As I've said before, I think Phase I Sharingan eyes are significantly weaker than the Sharingan's other phases, so it wouldn't take all that much effort before a Phase I Sharingan was pushed to its limits and could no longer handle the strain, thus the bleeding.
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So it makes sense that in Sarada's fight against a high-level opponent like Deepa or in training too long and hard, her Sharingan would bleed from the stress, strain, and overuse of having to perform things that a mere Phase I Sharingan is not really built to do. I would assume that if an Uchiha's eyes are bleeding, it is because they are putting too much strain on the eye, and so apparently Amaterasu nearly always puts too much strain on the eye.
