My story is similar to Mrs. Butterworth - I was not raised in the church. My father being a police officer who had run-ins with "Christians", and the examples that I saw all around me did not give me the best example or reason to believe - if these people were truly of God, then their lives would reflect it. (Which yes, it is by faith, and not by works... but there will be many who on that day, even though they say "Lord! Lord!", they will be turned away, and Jesus will say "I never knew you!" So-called faith without works is dead, empty, meaningless.)
At the same time, I intuitively knew that there was a god somewhere - as well as the deep inner knowledge and sense that there was more to life/existence/etc. than the hell that was Jr. high and high school, there was also the almost undeniable witness of the natural world. Granted, the atheist would say that the natural world denies the existence of God, but if you think about just how complex the inter-relationships of everything are - the fact that if one part of an ecosystem is removed, or one alien species is introduced, the entire system is thrown out of whack, or how life is even possible, especially life as complex as ours... I would say in considering that alone, there has to be some guiding force behind it.
Also, how I became a Christ Follower was not through friends or family bringing me to church, or anything like that, but a series of encounters with God that are undeniable to my mind. My first time going to church (at 18, which was also among my first positive encounters with Christians) was about a month and a half AFTER declaring my allegiance officially. I won't go into any further details regarding that here, but PM me if you want the whole story.
Now, as to whether or not Christianity or the Bible can be trusted... I do agree with those above that faith is important - but we must also remember that Christianity has only been around for about 2000 years. It is also not the only story of God's attempted relationship with humanity, lest we forget our Jewish brothers and sisters, who have been in relationship with the LORD for longer than us. However, these are reasons that seem to work:
1. Historical - there is historical evidence that do support the claims made by the Bible. There was a man named Jesus, the son of Joseph (actually, it would have been pronounced Yeshua, but that's a side-note), from Nazareth in the Galilee province, who was condemned to death by crucifixion by the Romans. There are also accounts during the early centuries of the movement, not just from Christians; also from the imperial powers, that attest to the curiosity, confusion, and even anger, caused by this movement. We also know that this movement started as a messianic/apocalyptic Jewish movement, which quickly spread into the Gentile world - and it went from being a laughed-at and persecuted minority to the most powerful (not to mention most numerous) religion in the world today, with about 70% of those being in Asia, Latin America and Africa.
2. In considering the teachings and prophecy found in Scripture (and by prophecy, I mean speaking for God, not foretelling the future like some fortune teller), the ideologies presented there, while often running counter to how we do things in the world, actually make a lot of sense. Give food to the hungry? Defend the widow and the orphan? Love your enemy (as opposed to hurting and killing them)? Forgive all debts every 7 years, and do not steal or covet each others' property? Treat one another as image-bearers of God? Care for the earth, and don't treat it like our own personal waste-basket? Be honest and have integrity? Makes a lot of sense to me.
3. Logical - while others may be better with this part than I am, I find myself amazed at how the Christian church not only got off the ground, but has continued despite wide-spread persecution in many places. How is it that a bunch of fishermen, farmers and prostitutes from a backwater part of the Roman empire, who were forced into hiding when their master and leader was killed (which happened a lot - and when it happened with most other messianic/apocalyptic figures, the followers usually disbanded), suddenly turn into a major missionary force, emboldened by accounts of the resurrection? (This is not even including the accounts of miracles that happened at that time, or that continued historically throughout church history - sorry, not a cessationist...
). And how is it in China, when all of the missionaries were forced to leave and all churches were forced to shut down at the risk of imprisonment or death, that the church shot from barely 10,000 including missionaries to over 100,000 native Chinese Christians in maybe 50 years? There is definitely something going on here that we may not be as familiar with in our spiritually-sanitized Western consciousness (at least not in our own day - history indicates otherwise...)
Sorry for the lengthy explanation. I hope what was said here could be of some assistance to you in your search.