The kind of prayer you will want to pray before studying the bible will very much depend on the context. Is this a personal bible study? In which case you may want to pray something that is open and vulnerable before God. Perhaps along the lines of the following:-
Lord, you know my heart,
and the times that I fail you and others.
I really need you now to speak to me through these words. Please inspire me in this time I have with you.
However, it may be that you are leading a group bible study, and there are people present who are guests, and not so familiar with religious terminology and language. It's very important to choose the words we use on these occassions carefully. (St Paul became "...all things to all people so that by all possible means I might save some.", 1 Cor 9:22
, NIV). Here's an example of a short prayer for a group bible study:-
Prayer for a Bible Study
God, you have made the heavens and the earth.
You have revealed your beauty in creation
and inspired the book that we are now about to study.
Please help us now as we read together.
Take us deeper into understanding more about you
and your love for us.
(a short prayer for a group bible study from www.lords-prayer-words.com)
Consider a short worship time before your study
It might be that a short time of worship would be appropriate before study. If this is the case, the psalms are a good starting point to aid worship. For example, you could read some of Psalm 63 to begin with:-
God—you’re my God!
I can’t get enough of you!
I’ve worked up such hunger and thirst for God,
traveling across dry and weary deserts.
2-4 So here I am in the place of worship, eyes open,
drinking in your strength and glory.
In your generous love I am really living at last!
My lips brim praises like fountains.
I bless you every time I take a breath;
My arms wave like banners of praise to you.
Psalm 63:1-4, (The Message)
You could then guide people by inviting them to spend a moment meditating on the words of these verses, and close the worship time with a short prayer, that will lead you into the study. For example:-
Thank you God that we are here, drinking in your presence. Please inspire us now as we read your word together.