There's never usually any implied washing after sleeping. You just become clean after long resting.
As far as what the blood is... Most likely there was some sort of effect wearing off that caused blood splatter (As it's after "Waking up" that the Long Rest occurs and active effects are removed and you're fully healed).
What the effect was? I haven't a clue. From what I recall, I don't remember any effect that causes blood splatter when fading - At least in the base game (I've had some modded abilities that did) - I only recall base game abilities that caused blood splatter while active (Warding Bond's shared damage causes blood splatter. Back when I used Astarion as a Bond Slave he'd always be standing in a pool of his own blood)
