There's a lot of non-Catholic Christians who have adopted the Catholic tradition (small "t" tradition) of observing Ash Wednesday.
However, there's also a lot of Christians who vehemently object to our Ash Wednesday liturgy. "Ash Wednesday is not in the Bible!" is the mantra of these folks.
From a website I found:
But guess what? Ash Wednesday is not in the Bible. Jesus never kept Ash Wednesday and neither did the apostles of the Early Church. If this “holy day” is a “Christian” ritual to remember Christ, then how come none of the disciples kept it after Jesus ascended to heaven? I’ve never read about Apostle Paul or John teaching in his letters to the churches about burning ashes and putting it on their foreheads.http://www.truthofgodthemother.com/ash-wednesday-another-non-biblical-holiday/
Firstly, we should ask these folks: why does every practice we do have to be found in the Bible? Does the Bible say that we're supposed to do this?
This meme by Catholic apologist Steve Ray could also apply to "Where is Ash Wednesday in the Bible?"
Secondly, we can point out that there's probably a whole lot of practices that they do which also aren't found in the Bible.
-Wednesday evening Bible studies
-having steeples on churches
-folding one's hands in prayer
-weddings in a church
-praying to the Holy Spirit
-wearing a wedding ring
And here's a lot of things these folks probably do that Jesus/Paul/John never did:
-attend a wedding on a beach
-sing hymns with an organ accompaniment
-preside at a wedding
-use a sound system at a prayer meeting
I also saw this from another website objecting to Ash Wednesday:
“When you fast,* do not look gloomy like the hypocrites. They neglect their appearance, so that they may appear to others to be fasting. Amen, I say to you, they have received their reward.But when you fast, anoint your head and wash your face,so that you may not appear to others to be fasting, except to your Father who is hidden. And your Father who sees what is hidden will repay you.--Matthew 6:16-18
I think the response to this is: if we are putting ashes on our foreheads to let the world know we are fasting, and therefore holier than everyone else who isn't fasting, then we are indeed "like the hypocrites". But I doubt any person walking around with ashes is doing this in the same way the hypocrites of Jesus' time did.
Finally, there are numerous references in the Bible to using ashes as a sign of repentance.
A Benjaminite fled from the battlefield and reached Shiloh that same day, with his clothes torn and his head covered with dirt.--1 Sam 4:12
Tamar put ashes on her head and tore the long tunic in which she was clothed.--2 Sam.13:19
Ashes also symbolize death and so remind us of our mortality. When the priest uses his thumb to sign one of the faithful with the ashes and says, "Remember, man, that thou art dust and unto dust thou shalt return," he is echoing God's address to Adam:
For you are dirt, and to dirt you shall return.--Gen. 3:19
And Abraham's confession: I am nothing but dust and ashes" --Gen. 18:27.
In short, Ash Wednesday is deeply rooted in Christian tradition/practice/custom and there's nothing we do in our Lenten obervations which is contrary to Scripture.