Is the church not to experience God in a "present way," or does it only need to be in a past tense manner through the Bible?
I had difficulty with your question because it was worded vaguely. The meaning changes depending on how you define the terms.
God is ever present in this world. "Even though I walk through the valley of the shadow of death, I fear no evil, for You are with me; Your rod and Your staff, they comfort me" (Psalms 23:4). God answers our prayers. "This is the confidence which we have before Him, that, if we ask anything according to His will, He hears us. And if we know that He hears us in whatever we ask, we know that we have the requests which we have asked from Him" (I John 5:14-15).
But typically people ignore these and think that God must supply miraculous gifts, as He did in the past, for His presence to be felt. God is present whether He supplies miraculous gifts or not. But God has been clear that the time of miraculous gifts has passed. See: Now Concerning Spiritual Gifts.