Humbling yourself means aknowledging our multitude of flaws and daily sins and, at the same time, knowing that we don't deserve what we ask for. It's telling God: "God, I'm a worm, not a man." (like some Orthodox fathers say, citing Psalm 22)
Praying boldly means aknowledging our multitude of flaws and daily sins, but, at the same time, being convinced that they have been covered by Jesus' sacrifice and, therefore, we deserve what we ask for because we ask it as children of God. It's telling God: "I'm Your son / daughter, bought with Jesus' blood."
Maybe it's just me, but I see a big difference between the two approaches.
There seems to be a difference in approach maybe, on some level, tied in to how the EO vs. some Protestants see our standing with God, salvation, and the purpose of the Christian life.
Someone correct me if I'm wrong, but the EO seem to see our lives in Christ as a journey of repentance, asceticism, prayer, and growing more like Christ.
It's a battle against sin and the flesh and the danger of Hell fire not yet completely won.
Many Protestants see our lives in Christ as enjoying and living assured in what we've already been given through faith, irrespective of anything we do or fail to do. We've already won, the battle's ours, and all we have to do in continue to have faith and proclaim the Blood of Christ over our past, present, and future sins.
So, there's a difference in perspective here. A big one. Protestants, especially Evangelical and Pentecostal Protestants, are making inroads into Eastern Orthodox countries, establishing churches, seeking to call the Eastern Orthodox into Evangelical Christianity, and sharing a very different message on salvation, what the Christian life is, and what we should do and believe as Christians.
So there are two very different systems of thought here. And I wonder if maybe being exposed to two different theologies is causing this confusion for you.