The Reverend Bryce Wandrey, Anglican priest & former Lutheran priest, has suggested that it is more appropriate to wipe off one's ashes from his forehead after Mass than to leave them on all day. I too have been thinking about this very issue lately, but my thinking has gone in the exact opposite direction.
Bryce is commendably concerned about a Christian sense of modesty, and about not wanting to unnecessarily advertise one's piety. More on that topic below. Bryce also sees his decision to wipe the ashes off right away when leaving church as based upon a literal reading of Matthew 6. I would respectfully suggest that such a reading might be literalistic, but not literal. That is to say, I do not see this text as speaking to the question of what Christians should do with the ashes that are ritually imposed upon them on Ash Wednesday. Indeed, it would be inappropriate to advertise our fasting by walking around with drooping, tired faces. Instead, the Christian who submits himself to rigorous fasting, and such a creature is rare today, does well to throw water on his face, and stand up straight before going out, lest his fasting become an overt boast, just as the one who shouts his prayers on the street corner is making his prayer an overt boast.
I would urge, in fact, that just as our Lord's words in Matthew 6 against those who pray "in the corners of the streets, that they may be seen of men," shouldn't keep Christians from praying (aloud, and with the sign of the cross) before and after meals when out in a restaurants, likewise His words in the same chapter against showing off one's fasting does not mean that we should be hesitant or timid to fast publicly.
Let me offer examples, to be very clear. When at a restaurant, it is not boasting or showing off one's fasting by asking the server for the vegetarian menu. It is not showing off when one orders the fish, even when everyone else at the table forgets that it's Friday, or it just isn't that important to them. It is neither condemning nor boasting on his part to try to remain true to such traditions. It is not boasting or showing off when one discusses the topic of fasting openly & publicly. In all of the above scenarios I have seen Lutherans condemn Catholics and other Lutherans wrongfully. There is no way to read the heart and the motives of those who behave in ways to which some may be unaccustomed. Rather, we should accept each other where we are at, and support each other.
Getting back to ashes in particular, this is not a custom that is really directly pertinent to fasting. It does imply it, in my opinion, but it should be considered as a slightly separate issue. Ashes are a sign, like the sign of the cross, which we also ought to be bold to practice in public. Wearing ashes is a sign and witness, both to ourselves, and to everyone who sees it. It is a sign of our penitence, our confession of our sinfulness and mortality, and yes, in a broader way, of our faith in Christ, and our allegiance to Christian tradition. For all of these reasons, I suggest it is good, right, and salutary to keep the ashes on one's forehead until getting ready for bed, even it they were imposed at an early morning Mass.