The root cause of the CWE-125 (Out-of-bounds Read) vulnerability in the given code slice is:

The code attempts to dereference the pointer 'col_sep_string' without first checking if it's null or valid. If 'col_sep_string' is null or points to an invalid memory location, attempting to access its first character using '*col_sep_string' will result in an out-of-bounds read.

This vulnerability occurs because:

1. There's no prior null check or validation of 'col_sep_string' before dereferencing it.
2. The code assumes that 'col_sep_string' always points to a valid, null-terminated string.
3. If 'col_sep_string' is null or points to an invalid memory location, accessing '*col_sep_string' will attempt to read from an out-of-bounds memory address.

To fix this vulnerability, the code should include a null check and ensure 'col_sep_string' points to a valid memory location before dereferencing it. Additionally, it should validate that the string has at least one character before attempting to access its first element.