Wearing ash on your head in public is ok if you mean it as as a sign of penitence - as a way of saying “I am a sinner”.
It is not ok if you mean it as a way of saying “I am fasting, look at me!”. Much better in that case to avoid the risk of Phariseeism and wash it off.
As always it is not the sign, but what is going on in the interior that matters.
I hope Biden meant it as a sign of inward humility and repentance. For all his faults it is at least plausible. Whereas - imagine Clinton or Obama with the ash on their face.
The priest at my old Episcopal church said that if you feel conspicuous and really want to wash it off, then leave it on. But, if you’re feeling kind of good about yourself and want to leave it on, then wash it off. ;-)
Sounds like a good rule to me! I left mine on the first half of the day because of where I was and who I was around, then I washed it off the second half of the day because I was in a different place around different people.