To me, personally, saying I am a "non-denominational Christian" sounds like I can't make up my mind and it has allowed me to be stagnant in my spiritual growth.
Really, there is no such thing as a "non-denominational" church. Every church has a statement of faith or belief and the members of that congregation typically will follow that. There are many "Christian" churches or "Churches of Christ" where I live and if you ask them about a catechism or statement of faith, they will say that they believe in the Bible, of course. In many of these churches, they will have select Bible verses posted on the walls of their fellowship hall or gym. Usually, these verses boil down to salvation being through faith alone; the Bible being the inerrant word of God; and people going to a real hell or heaven after death. While these churches have no organization or ties to other churches, really they share the same creed and are therefore part of a loose denomination, even if they consider themselves "non-denominational."
Here is an example of a typical non-denominational church:
Our Mission
It’s simple. We exist to bring people to Christ and build them in His image.
That Jesus is God's Son and the only means of seeing God and Heaven.
(John 3:16, 14:6; Acts 4:12)
That the Bible is God's inspired Word.
(Psalms 119:105; 2 Timothy 3:16)
That man was created by and for God, but that all have sinned and fall short of God's glorious standard.
(Romans 3:23, 6:23)
That those obeying Jesus and accepting His gift of salvation from sin and it's consequences should, turn from their sins, confess their faith in Christ, and be baptized.
(Acts 2:38, 8:35-38, 22:16)
That the church on earth is the Body of Christ, empowered by the Holy Spirit to carry out the will and work of Jesus.
(Ephesians 4:1-16)
That Jesus will one day return to earth to take His faithful church to Heaven.
(John 14:2,3; 1 Thessalonians 4:13-18)