Many Bible colleges have an official relationship with a particular church denomination, either through a governing body or theological oversight. Other Christian colleges may have a looser affiliation or informal connection with a church denomination.
As you search for a Bible college, accredited or otherwise, the Christian college and denomination they are affiliated with may be independent of each other. Some colleges may have ties or affiliations with several churches or Christian traditions.
Most Bible colleges will accept you regardless of your church affiliation. However, they may require a statement of faith or testimony of how you became a Christian. Also, there may be rules and standards that you are required to adhere to. Each Bible institution will set their own standards, usually based on the Bible.